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Wyniki wyszukiwania dla: INDEPENDENCE NUMBER, GREEDY ALGORITHM, GRAPH HARD-TO-PROCESS
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On Tradeoffs Between Width- and Fill-like Graph Parameters
PublikacjaIn this work we consider two two-criteria optimization problems: given an input graph, the goal is to find its interval (or chordal) supergraph that minimizes the number of edges and its clique number simultaneously. For the interval supergraph, the problem can be restated as simultaneous minimization of the path width pw(G) and the profile p(G) of the input graph G. We prove that for an arbitrary graph G and an integer t ∈ {1,...
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Some variants of perfect graphs related to the matching number, the vertex cover and the weakly connected domination number
PublikacjaGiven two types of graph theoretical parameters ρ and σ, we say that a graph G is (σ, ρ)- perfect if σ(H) = ρ(H) for every non-trivial connected induced subgraph H of G. In this work we characterize (γw, τ )-perfect graphs, (γw, α′)-perfect graphs, and (α′, τ )-perfect graphs, where γw(G), τ (G) and α′(G) denote the weakly connected domination number, the vertex cover number and the matching number of G, respectively. Moreover,...
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Interval incidence coloring of bipartite graphs
PublikacjaIn this paper we study the problem of interval incidence coloring of bipartite graphs. We show the upper bound for interval incidence coloring number (χii) for bipartite graphs χii≤2Δ, and we prove that χii=2Δ holds for regular bipartite graphs. We solve this problem for subcubic bipartite graphs, i.e. we fully characterize the subcubic graphs that admit 4, 5 or 6 coloring, and we construct a linear time exact algorithm for subcubic...
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On-line Search in Two-Dimensional Environment
PublikacjaWe consider the following on-line pursuit-evasion problem. A team of mobile agents called searchers starts at an arbitrary node of an unknown network. Their goal is to execute a search strategy that guarantees capturing a fast and invisible intruder regardless of its movements using as few searchers as possible. We require that the strategy is connected and monotone, that is, at each point of the execution the part of the graph...
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Total Completion Time Minimization for Scheduling with Incompatibility Cliques
PublikacjaThis paper considers parallel machine scheduling with incompatibilities between jobs. The jobs form a graph equivalent to a collection of disjoint cliques. No two jobs in a clique are allowed to be assigned to the same machine. Scheduling with incompatibilities between jobs represents a well-established line of research in scheduling theory and the case of disjoint cliques has received increasing attention in recent...
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Infinite chromatic games
PublikacjaIn the paper we introduce a new variant of the graph coloring game and a new graph parameter being the result of the new game. We study their properties and get some lower and upper bounds, exact values for complete multipartite graphs and optimal, often polynomial-time strategies for both players provided that the game is played on a graph with an odd number of vertices. At the end we show that both games, the new and the classic...
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Some Progress on Total Bondage in Graphs
PublikacjaThe total bondage number b_t(G) of a graph G with no isolated vertex is the cardinality of a smallest set of edges E'⊆E(G) for which (1) G−E' has no isolated vertex, and (2) γ_t(G−E')>γ_t(G). We improve some results on the total bondage number of a graph and give a constructive characterization of a certain class of trees achieving the upper bound on the total bondage number.
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Optimal backbone coloring of split graphs with matching backbones
PublikacjaFor a graph G with a given subgraph H, the backbone coloring is defined as the mapping c: V(G) -> N+ such that |c(u)-c(v)| >= 2 for each edge uv \in E(H) and |c(u)-c(v)| >= 1 for each edge uv \in E(G). The backbone chromatic number BBC(G;H) is the smallest integer k such that there exists a backbone coloring with max c(V(G)) = k. In this paper, we present the algorithm for the backbone coloring of split graphs with matching backbone.
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Equitable coloring of corona multiproducts of graphs
PublikacjaWe give some results regarding the equitable chromatic number for l-corona product of two graphs: G and H, where G is an equitably 3- or 4-colorable graph and H is an r-partite graph, a cycle or a complete graph. Our proofs lead to polynomial algorithms for equitable coloring of such graph products provided that there is given an equitable coloring of G.
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Weighted 2-sections and hypergraph reconstruction
PublikacjaIn the paper we introduce the notion of weighted 2-sections of hypergraphs with integer weights and study the following hypergraph reconstruction problems: (1) Given a weighted graph , is there a hypergraph H such that is its weighted 2-section? (2) Given a weighted 2-section , find a hypergraph H such that is its weighted 2-section. We show that (1) is NP-hard even if G is a complete graph or integer weights w does not exceed...
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2-outer-independent domination in graphs
PublikacjaWe initiate the study of 2-outer-independent domination in graphs. A 2-outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of V(G)\D has at least two neighbors in D, and the set V(G)\D is independent. The 2-outer-independent domination number of a graph G is the minimum cardinality of a 2-outer-independent dominating set of G. We show that if a graph has minimum degree at least two,...
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Dataset of non-isomorphic graphs being coloring types (K5-e,Km-e;n), 2<m<5, 1<n<R(K5-e,Km-e)
Dane BadawczeFor K5-e and Km-e graphs, the type coloring (K5-e,Km-e;n) is such an edge coloring of the full Kn graph, which does not have the K5-e subgraph in the first color (no edge in the graph) or the Km-e subgraph in the second color (exists edge in the graph). Km-e means the full Km graph with one edge removed.The Ramsey number R(K5-e,Km-e) is the smallest...
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Dataset of non-isomorphic graphs being coloring types (K6-e,Km-e;n), 2<m<5, 1<n<R(K6-e,Km-e)
Dane BadawczeFor K6-e and Km-e graphs, the type coloring (K6-e,Km-e;n) is such an edge coloring of the full Kn graph, which does not have the K6-e subgraph in the first color (no edge in the graph) or the Km-e subgraph in the second color (exists edge in the graph). Km-e means the full Km graph with one edge removed. The Ramsey number R(K6-e,Km-e) is the smallest...
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Dataset of non-isomorphic graphs of the coloring types (K4,Km-e;n), 2<m<5, 1<n<R(K4,Km-e)
Dane BadawczeFor K4 and Km-e graphs, a coloring type (K4,Km-e;n) is such an edge coloring of the full Kn graph, which does not have the K4 subgraph in the first color (representing by no edges in the graph) or the Km-e subgraph in the second color (representing by edges in the graph). Km-e means the full Km graph with one edge removed.The Ramsey number R(K4,Km-e)...
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Statistics of AFM current-voltage curves
Dane BadawczeMapping surface electrical conductivity offers enormous cognitive possibilities regarding the structure and properties of modern materials. The technique invented for this purpose (Conductive AFM) by Murrel's team and colleagues allows independent monitoring of the local conductivity of materials in correlation with the topographic profile. The mentioned...
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On minimum cost edge searching
PublikacjaWe consider the problem of finding edge search strategies of minimum cost. The cost of a search strategy is the sum of searchers used in the clearing steps of the search. One of the natural questions is whether it is possible to find a search strategy that minimizes both the cost and the number of searchers used to clear a given graph G. We call such a strategy ideal. We prove, by an example, that ideal search strategies do not...
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Restrained differential of a graph
PublikacjaGiven a graph $G=(V(G), E(G))$ and a vertex $v\in V(G)$, the {open neighbourhood} of $v$ is defined to be $N(v)=\{u\in V(G) :\, uv\in E(G)\}$. The {external neighbourhood} of a set $S\subseteq V(G)$ is defined as $S_e=\left(\cup_{v\in S}N(v)\right)\setminus S$, while the \emph{restrained external neighbourhood} of $S$ is defined as $S_r=\{v\in S_e : N(v)\cap S_e\neq \varnothing\}$. The restrained differential of a graph $G$ is...
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Total chromatic sum for trees
PublikacjaThe total chromatic sum of a graph is the minimum sum of colors (natural numbers) taken over all proper colorings of vertices and edges of a graph. We provide infinite families of trees for which the minimum number of colors to achieve the total chromatic sum is equal to the total chromatic number. We construct infinite families of trees for which these numbers are not equal, disproving the conjecture from 2012.
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On extremal sizes of locally k-tree graphs
PublikacjaA graph G is a locally k-tree graph if for any vertex v the subgraph induced by the neighbours of v is a k-tree, k>=0, where 0-tree is an edgeless graph, 1-tree is a tree. We characterize the minimum-size locally k-trees with n vertices. The minimum-size connected locally k-trees are simply (k + 1)-trees. For k >= 1, we construct locally k-trees which are maximal with respect to the spanning subgraph relation. Consequently, the...
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On the Characteristic Graph of a Discrete Symmetric Channel
PublikacjaWe present some characterizations of characteristic graphs of row and/or column symmetric channels. We also give a polynomial-time algorithm that decides whether there exists a discrete symmetric channel whose characteristic graph is equal to a given input graph. In addition, we show several applications of our results.
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Dataset of non-isomorphic graphs of the coloring types (Km,K3-e;n), 4<m<8, 1<n<R(Km,K3-e)
Dane BadawczeFor Km and K3-e graphs, a coloring type (Km,K3-e;n) is such an edge coloring of the full Kn graph, which does not have the Km subgraph in the first color (representing by no edges in the graph) or the K3-e subgraph in the second color (representing by edges in the graph). K3-e means the full Km graph with one edge removed.The Ramsey number R(Km,K3-e)...
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Independent Domination Subdivision in Graphs
PublikacjaA set $S$ of vertices in a graph $G$ is a dominating set if every vertex not in $S$ is adjacent to a vertex in~$S$. If, in addition, $S$ is an independent set, then $S$ is an independent dominating set. The independent domination number $i(G)$ of $G$ is the minimum cardinality of an independent dominating set in $G$. The independent domination subdivision number $\sdi(G)$ is the minimum number of edges that must be subdivided (each...
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An Alternative Proof of a Lower Bound on the 2-Domination Number of a Tree
PublikacjaA 2-dominating set of a graph G is a set D of vertices of G such that every vertex not in D has a at least two neighbors in D. The 2-domination number of a graph G, denoted by gamma_2(G), is the minimum cardinality of a 2-dominating set of G. Fink and Jacobson [n-domination in graphs, Graph theory with applications to algorithms and computer science, Wiley, New York, 1985, 283-300] established the following lower bound on the 2-domination...
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Graphs with isolation number equal to one third of the order
PublikacjaA set D of vertices of a graph G is isolating if the set of vertices not in D and with no neighbor in D is independent. The isolation number of G, denoted by \iota(G) , is the minimum cardinality of an isolating set of G. It is known that \iota(G) \leq n/3 , if G is a connected graph of order n, , distinct from C_5 . The main result of this work is the characterisation of unicyclic and block graphs of order n with isolating number...
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2-Coloring number revisited
Publikacja2-Coloring number is a parameter, which is often used in the literature to bound the game chromatic number and other related parameters. However, this parameter has not been precisely studied before. In this paper we aim to fill this gap. In particular we show that the approximation of the game chromatic number by the 2-coloring number can be very poor for many graphs. Additionally we prove that the 2-coloring number may grow...
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Edge subdivision and edge multisubdivision versus some domination related parameters in generalized corona graphs
PublikacjaGiven a graph G= (V, E), the subdivision of an edge e=uv∈E(G) means the substitution of the edge e by a vertex x and the new edges ux and xv. The domination subdivision number of a graph G is the minimum number of edges of G which must be subdivided (where each edge can be subdivided at most once) in order to increase the domination number. Also, the domination multisubdivision number of G is the minimum number of subdivisions...
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How to meet when you forget: log-space rendezvous in arbitrary graphs
PublikacjaTwo identical (anonymous) mobile agents start from arbitrary nodes in an a priori unknown graph and move synchronously from node to node with the goal of meeting. This rendezvous problem has been thoroughly studied, both for anonymous and for labeled agents, along with another basic task, that of exploring graphs by mobile agents. The rendezvous problem is known to be not easier than graph exploration. A well-known recent result...
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Dataset of non-isomorphic graphs of the coloring types (K3,Km-e;n), 2<m<7, 1<n<R(K3,Km-e).
Dane BadawczeFor K3 and Km-e graphs, a coloring type (K3,Km-e;n) is such an edge coloring of the full Kn graph, which does not have the K3 subgraph in the first color (representing by no edges in the graph) or the Km-e subgraph in the second color (representing by edges in the graph). Km-e means the full Km graph with one edge removed.The Ramsey number R(K3,Km-e)...
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Double bondage in graphs
PublikacjaA vertex of a graph is said to dominate itself and all of its neighbors. A double dominating set of a graph G=(V,E) is a set D of vertices of G such that every vertex of G is dominated by at least two vertices of D. The double domination number of a graph G, denoted by gamma_d(G), is the minimum cardinality of a double dominating set of G. The double bondage number of G, denoted by b_d(G), is the minimum cardinality among all sets...
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Dataset of non-isomorphic graphs of the coloring types (K3,Km;n), 2<m<7, 1<n<R(3,m)
Dane BadawczeFor K3 and Km graphs, a coloring type (K3,Km;n) is such an edge coloring of the full Kn graph, which does not have the K3 subgraph in the first color (representing by no edges in the graph) or the Km subgraph in the second color (representing by edges in the graph).The Ramsey number R(3,m) is the smallest natural number n such that for any edge coloring...
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Minimum order of graphs with given coloring parameters
PublikacjaA complete k-coloring of a graph G=(V,E) is an assignment F: V -> {1,...,k} of colors to the vertices such that no two vertices of the same color are adjacent, and the union of any two color classes contains at least one edge. Three extensively investigated graph invariants related to complete colorings are the minimum and maximum number of colors in a complete coloring (chromatic number χ(G) and achromatic number ψ(G), respectively),...
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On trees with double domination number equal to 2-domination number plus one
PublikacjaA vertex of a graph is said to dominate itself and all of its neighbors. A subset D subseteq V(G) is a 2-dominating set of G if every vertex of V(G)D is dominated by at least two vertices of D, while it is a double dominating set of G if every vertex of G is dominated by at least two vertices of D. The 2-domination (double domination, respectively) number of a graph G is the minimum cardinality of a 2-dominating (double dominating,...
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On trees attaining an upper bound on the total domination number
PublikacjaA total dominating set of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D. The total domination number of a graph G, denoted by γ_t(G), is the minimum cardinality of a total dominating set of G. Chellali and Haynes [Total and paired-domination numbers of a tree, AKCE International Journal of Graphs and Combinatorics 1 (2004), 69-75] established the following upper bound on the total domination...
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2-bondage in graphs
PublikacjaA 2-dominating set of a graph G=(V,E) is a set D of vertices of G such that every vertex of V(G)D has at least two neighbors in D. The 2-domination number of a graph G, denoted by gamma_2(G), is the minimum cardinality of a 2-dominating set of G. The 2-bondage number of G, denoted by b_2(G), is the minimum cardinality among all sets of edges E' subseteq E such that gamma_2(G-E') > gamma_2(G). If for every E' subseteq E we have...
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Neural Network-Based Sequential Global Sensitivity Analysis Algorithm
PublikacjaPerforming global sensitivity analysis (GSA) can be challenging due to the combined effect of the high computational cost, but it is also essential for engineering decision making. To reduce this cost, surrogate modeling such as neural networks (NNs) are used to replace the expensive simulation model in the GSA process, which introduces the additional challenge of finding the minimum number of training data samples required to...
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Rendezvous of Distance-Aware Mobile Agents in Unknown Graphs
PublikacjaWe study the problem of rendezvous of two mobile agents starting at distinct locations in an unknown graph. The agents have distinct labels and walk in synchronous steps. However the graph is unlabelled and the agents have no means of marking the nodes of the graph and cannot communicate with or see each other until they meet at a node. When the graph is very large we want the time to rendezvous to be independent of the graph size...
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Drawing maps with advice
PublikacjaW pracy podejmujemy temat konstrukcji algorytmu dla agenta, który zostaje umieszczony w dowolnym wierzchołku grafu (wierzchołki są nierozróżnialne, krawędzie mają etykiety portów), po czym realizuje algorytm zmierzający do znalezienia drzewa spinającego grafu lub izomorficznej kopii grafu. Dla obu problemów podajemy asymptotycznie dokładne lub prawie dokładne oszacowania na ilość bitów dodatkowej informacji, którą agent musi otrzymać...
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Dataset of non-isomorphic graphs being coloring types (K4-e,Km-e;n), 2<m<7, 1<n<R(K4-e,Km-e)
Dane BadawczeFor K4-e and Km-e graphs, the type coloring (K4-e,Km-e;n) is such an edge coloring of the full Kn graph, which does not have the K4-e subgraph in the first color (no edge in the graph) or the Km-e subgraph in the second color (exists edge in the graph). Km-e means the full Km graph with one edge removed.The Ramsey number R(K4-e,Km-e) is the smallest...
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Fast Calibration-Free Single-Anchor Indoor Localization Based on Limited Number of ESPAR Antenna Radiation Patterns
Publikacja— In this article, we investigate how the calibrationfree single-anchor indoor localization algorithm developed for base stations equipped with electronically steerable parasitic array radiator (ESPAR) antennas can further be improved. By reducing the total number of ESPAR antenna radiation patterns used in localization process, one can significantly reduce the time needed for an object localization. Performed localization measurements...
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Equitable coloring of corona products of graphs
PublikacjaIn this paper we consider an equitable coloring of some corona products of graphs G and H in symbols, G o H). In particular, we show that deciding the colorability of G o H is NP-complete even if G is 4-regular and H is K_2. Next, we prove exact values or upper bounds on the equitable chromatic number of G o H, where G is an equitably 3- or 4-colorable graph and H is an r-partite graph, a path, a cycle or a complete graph.
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Weakly convex and convex domination numbers of some products of graphs
PublikacjaIf $G=(V,E)$ is a simple connected graph and $a,b\in V$, then a shortest $(a-b)$ path is called a $(u-v)$-{\it geodesic}. A set $X\subseteq V$ is called {\it weakly convex} in $G$ if for every two vertices $a,b\in X$ exists $(a-b)$- geodesic whose all vertices belong to $X$. A set $X$ is {\it convex} in $G$ if for every $a,b\in X$ all vertices from every $(a-b)$-geodesic belong to $X$. The {\it weakly convex domination number}...
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Bounds on the cover time of parallel rotor walks
PublikacjaThe rotor-router mechanism was introduced as a deterministic alternative to the random walk in undirected graphs. In this model, a set of k identical walkers is deployed in parallel, starting from a chosen subset of nodes, and moving around the graph in synchronous steps. During the process, each node successively propagates walkers visiting it along its outgoing arcs in round-robin fashion, according to a fixed ordering. We consider...
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An Efficient Noisy Binary Search in Graphs via Median Approximation
PublikacjaConsider a generalization of the classical binary search problem in linearly sorted data to the graph-theoretic setting. The goal is to design an adaptive query algorithm, called a strategy, that identifies an initially unknown target vertex in a graph by asking queries. Each query is conducted as follows: the strategy selects a vertex q and receives a reply v: if q is the target, then =, and if q is not the target, then v is a...
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Asynchronous Networked Estimation System for Continuous Time Stochastic Processes
PublikacjaIn this paper we examine an asynchronous networked estimation system for state estimation of continuous time stochastic processes. Such a system is comprised of several estimation nodes connected using a possibly incomplete communication graph. Each of the nodes uses a Kalman filter algorithm and data from a local sensor to compute local state estimates of the process under observation. It also performs data fusion of local estimates...
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Dataset of non-isomorphic graphs being coloring types (K3-e,Km-e;n), 2<m<8, 1<n<R(K3-e,Km-e)
Dane BadawczeFor K3-e and Km-e graphs, the type coloring (K3-e,Km-e;n) is such an edge coloring of the full Kn graph, which does not have the K3-e subgraph in the first color (no edge in the graph) or the Km-e subgraph in the second color (exists edge in the graph). Km-e means the full Km graph with one edge removed.The Ramsey number R(K3-e,Km-e) is the smallest...
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Parallel tabu search for graph coloring problem
PublikacjaTabu search is a simple, yet powerful meta-heuristic based on local search that has been often used to solve combinatorial optimization problems like the graph coloring problem. This paper presents current taxonomy of patallel tabu search algorithms and compares three parallelization techniques applied to Tabucol, a sequential TS algorithm for graph coloring. The experimental results are based on graphs available from the DIMACS...
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The computational complexity of the backbone coloring problem for planar graphs with connected backbones
PublikacjaIn the paper we study the computational complexity of the backbone coloring problem for planar graphs with connected backbones. For every possible value of integer parameters λ≥2 and k≥1 we show that the following problem: Instance: A simple planar graph GG, its connected spanning subgraph (backbone) HH. Question: Is there a λ-backbone coloring c of G with backbone H such that maxc(V(G))≤k? is either NP-complete or polynomially...
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Total domination in versus paired-domination in regular graphs
PublikacjaA subset S of vertices of a graph G is a dominating set of G if every vertex not in S has a neighbor in S, while S is a total dominating set of G if every vertex has a neighbor in S. If S is a dominating set with the additional property that the subgraph induced by S contains a perfect matching, then S is a paired-dominating set. The domination number, denoted γ(G), is the minimum cardinality of a dominating set of G, while the...
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Automatic evaluation of information credibility in Semantic Web and Knowledge Grid
PublikacjaThis article presents a novel algorithm for automatic estimation of information credibility. It concerns information collected in Knowledge Grid and Semantic Web. Possibilities to evaluate the credibility of information in such structures are much greater than those available for WWW sites which use natural language. The rating system presented in this paper estimates credibility automatically on the basis of the following metrics:...
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Data obtained by computation for X-ray imaging of grating without magnification using oriented Gaussian beams
Dane BadawczeThe propagation of X-ray waves through an optical system consisting of grating and X-ray refractive lenses is considered. In this approach, the propagating wave is represented as a superposition of the oriented Gaussian beams. The direction of wave propagation in each Gaussian beam is consistent with the local propagation direction of the X-ray wavefront.