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Search results for: ALGORITHMIC GRAPH THEORY
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Discussiones Mathematicae Graph Theory
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Workshop on Graph Theory
EventsThe Gdańsk Workshop on Graph Theory (GWGT) is an annual, informal workshop whose goal is to provide a forum for scientists to meet, present their work, interact, and establish collaborations in the field of Graph Theory
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KOALA Graph Theory Internet Service
PublicationKOALA has been created with the idea of C++ library templates, implementing a broad set of procedures in the fields of algorithmic graph theory and network problems in discreate optimization. During the C2NIWA project, a library has been greatly ectended, the code refactored and enclosed with the internet service available in the public repository of thr project. Today it contains interconnected educational materials in the form...
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Product Graph Invariants with Applications in the Theory of Information
PublicationThere are a large number of graph invariants. In the paper, we consider some of them, e.g. the independence and chromatic numbers. It is well know that we cannot efficiently calculate these numbers for arbitrary graphs. In the paper we present relations between these invariants and concepts from the theory of information. Concepts such as source coding and transmission over a noisy channel with zero probability of error are modeled...
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Modeling the impact of surface currents in a harbor using graph theory
PublicationEnsuring security in a harbor requires research into its infrastructure using spatial environmental data. This paper presents a methodology that defines the design of a graph for modeling the interactions between surface currents and moving objects. Combining this graph with port charts that integrate electronic navigation charts with coastal orthophotographs allows us to perform a multidimensional analysis. In addition, the complete...
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Electronic Journal of Graph Theory and Applications
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Application of Graph Theory Algorithms in Non-disjoint Functional Decomposition of Specific Boolean Functions
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International Journal of Combinatorial Graph Theory and Applications
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JOURNAL OF GRAPH THEORY
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Algorithmic Learning Theory
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Topological and Geometric Graph Theory
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Techniques and Problems in Graph Theory
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Workshop on Probabilistic Graph Theory
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International Symposium on Algorithmic Game Theory
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Conference on Graph Theory and Discrete Geometry
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EuroConference on Combinatorics, Graph Theory and Applications
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Workshop on Computational Graph Theory and Combinatorics
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TAI: Algorithmic Information Theory: Kolmogorov Complexity
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South African International Graph Theory Conference
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Southeastern International Conference on Combinatorics, Graph Theory, and Computing
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Kyoto International Conference on Computational Geometry and Graph Theory
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The Potential of Greed for Independence
PublicationThe well-known lower bound on the independence number of a graph due to Caro and Wei can be established as a performance guarantee of two natural and simple greedy algorithms or of a simple randomized algorithm. We study possible generalizations and improvements of these approaches using vertex weights and discuss conditions on so-called potential functions p(G) : V(G) -> N_0 defined on the vertex set of a graph G for which suitably...
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Restrained differential of a graph
PublicationGiven 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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Graph classes generated by Mycielskians
PublicationIn this paper we use the classical notion of weak Mycielskian M'(G) of a graph G and the following sequence: M'_{0}(G) =G, M'_{1}(G)=M'(G), and M'_{n}(G)=M'(M'_{n−1}(G)), to show that if G is a complete graph oforder p, then the above sequence is a generator of the class of p-colorable graphs. Similarly, using Mycielskian M(G) we show that analogously defined sequence is a generator of the class consisting of graphs for which the...
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TOTAL DOMINATION MULTISUBDIVISION NUMBER OF A GRAPH
PublicationThe domination multisubdivision number of a nonempty graph G was defined in [3] as the minimum positive integer k such that there exists an edge which must be subdivided k times to increase the domination number of G. Similarly we define the total domination multisubdivision number msd_t (G) of a graph G and we show that for any connected graph G of order at least two, msd_t (G) ≤ 3. We show that for trees the total domination...
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Relations between the domination parameters and the chromatic index of a graph
PublicationIn this paper we show bounds for the sum and the product of the domination parameters and the chromatic index of a graph. We alsopresent some families of graphs for which these bounds are achieved.
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Nordhaus-Gaddum results for the weakly convex domination number of a graph
PublicationArtykuł dotyczy ograniczenia z góry i z dołu (ze względu na ilość wierzchołków) sumy i iloczynu liczb dominowania wypukłego grafu i jego dopełnienia.
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Preface of guest editors
PublicationA special issue of Discussiones Mathematice Graph Theory (DMGT) is dedicated to selected papers presented at the 12th Workshop on Graph Theory: Colourings, Independence and Domination (CID) held on 16-21 September 2007 in Karpacz, Poland. It continues a series of international workshops: 1993-1997 in Lubiatów, 1998-2001 in Gronów, 2003 and 2005 in Karpacz. About 70 participants formed the audience of six invited lectures and 68...
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Preface
PublicationThis special issue of Discussiones Mathematice Graph Theory (DMGT) is dedicated to selected papers presented at the 13th Workshop on Graph Theory: Colourings, Independence and Domination (CID) held on 18-23 September 2009 in Szklarska Poręba, Poland. It continues a series of international workshops: 1993-1997 in Lubiatów, 1998-2001 in Gronów, and 2003-2007 in Karpacz. The meeting was organized by the Faculty of Mathematics, Computer...
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Total domination in versus paired-domination in regular graphs
PublicationA 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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Equitable coloring of corona multiproducts of graphs
PublicationWe 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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Workshop on Applications of Graph Theory in Wireless Ad hoc Networks and Sensor Networks
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Domination subdivision and domination multisubdivision numbers of graphs
PublicationThe domination subdivision number sd(G) of a graph G is the minimum number of edges that must be subdivided (where an edge can be subdivided at most once) in order to increase the domination number of G. It has been shown [10] that sd(T)<=3 for any tree T. We prove that the decision problem of the domination subdivision number is NP-complete even for bipartite graphs. For this reason we define the domination multisubdivision number...
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Interval incidence coloring of subcubic graphs
PublicationIn this paper we study the problem of interval incidence coloring of subcubic graphs. In [14] the authors proved that the interval incidence 4-coloring problem is polynomially solvable and the interval incidence 5-coloring problem is N P-complete, and they asked if χii(G) ≤ 2∆(G) holds for an arbitrary graph G. In this paper, we prove that an interval incidence 6-coloring always exists for any subcubic graph G with ∆(G) = 3.
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A note on polynomial algorithm for cost coloring of bipartite graphs with Δ ≤ 4
PublicationIn the note we consider vertex coloring of a graph in which each color has an associated cost which is incurred each time the color is assigned to a vertex. The cost of coloring is the sum of costs incurred at each vertex. We show that the minimum cost coloring problem for n-vertex bipartite graph of degree ∆≤4 can be solved in O(n^2) time. This extends Jansen’s result [K.Jansen,The optimum cost chromatic partition problem, in:...
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On incidence coloring of coloring of complete multipartite and semicubic bipartite graphs
PublicationIn the paper, we show that the incidence chromatic number of a complete k-partite graph is at most ∆+2 (i.e., proving the incidence coloring conjecture for these graphs) and it is equal to ∆+1 if and only if the smallest part has only one vertex.
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Block graphs with large paired domination multisubdivision number
PublicationThe paired domination multisubdivision number of a nonempty graph G, denoted by msdpr(G), is the smallest positive integer k such that there exists an edge which must be subdivided k times to increase the paired domination number of G. It is known that msdpr(G) ≤ 4 for all graphs G. We characterize block graphs with msdpr(G) = 4.
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Parity vertex colouring of graphs
PublicationA parity path in a vertex colouring of a graph is a path along which each colour is used an even number of times. Let Xp(G) be the least number of colours in a proper vertex colouring of G having no parity path. It is proved that for any graph G we have the following tight bounds X(G) <= Xp(G) <=|V(G)|− a(G)+1, where X(G) and a(G) are the chromatic number and the independence number of G, respectively. The bounds are improved for...
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T-colorings, divisibility and circular chromatic number
PublicationLet T be a T-set, i.e., a finite set of nonnegative integers satisfying 0 ∈ T, and G be a graph. In the paper we study relations between the T-edge spans espT (G) and espd⊙T (G), where d is a positive integer and d ⊙ T = {0 ≤ t ≤ d (max T + 1): d |t ⇒ t/d ∈ T} . We show that espd⊙T (G) = d espT (G) − r, where r, 0 ≤ r ≤ d − 1, is an integer that depends on T and G. Next we focus on the case T = {0} and show that espd⊙{0} (G) =...
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Optimal backbone coloring of split graphs with matching backbones
PublicationFor 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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On-line P-coloring of graphs
PublicationFor a given induced hereditary property P, a P-coloring of a graph G is an assignment of one color to each vertex such that the subgraphs induced by each of the color classes have property P. We consider the effectiveness of on-line P-coloring algorithms and give the generalizations and extensions of selected results known for on-line proper coloring algorithms. We prove a linear lower bound for the performance guarantee function...
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Efficient list cost coloring of vertices and/or edges of bounded cyclicity graphs
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Trees with equal restrained domination and total restrained domination numbers
PublicationW publikacji scharakteryzowano wszystkie drzewa, w których liczby dominowania powściągniętego oraz podwójnie totalnego są sobie równe.
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Efficient list cost coloring of vertices and/or edges of bounded cyclicity graphs
PublicationW artykule rozważamy listowo-kosztowe kolorowanie wierzchołków i krawędzi grafu w modelu wierzchołkowym, krawędziowym, totalnym i pseudototalnym. Stosujemy programowanie dynamiczne w celu otrzymania algorytmów wielomianowych dla drzew. Następnie uogólniamy to podejście na dowolne grafy z ograniczonymi liczbami cyklomatycznymi i na ich multikolorowania.
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Graphs with equal domination and 2-distance domination numbers
PublicationW publikacji scharakteryzowane są wszystkie te drzewa i grafy jednocykliczne, w których liczba dominowania oraz liczba 2-dominowania na odległość są sobie równe.
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Minimum vertex ranking spanning tree problem for chordal and proper interval graphs
PublicationW pracy rozważamy problem szukania, dla danego grafu prostego, drzewa spinającego, którego uporządkowana liczba chromatyczna jest minimalna. K.~Miyata i inni dowiedli w [Np-hardness proof and an approximation algorithm for the minimum vertex ranking spanning tree problem,Discrete Appl. Math. 154 (2006) 2402-2410], że odpowiedni problem decyzyjny jest NP-trudny już w przypadku pytania o istnienie uporządkowanego 4-pokolorowania....
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Weakly connected domination subdivision numbers
PublicationLiczba podziału krawędzi dla dominowania słabo spójnego to najmniejsza liczba krawędzi jaką należy podzielić, aby wzrosła liczba dominowania słabo wypukłego. W pracy przedstawione są własności liczby podziału krawędzi dla dominowania słabo spójnego dla różnych grafów.
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Total outer-connected domination in trees
PublicationW pracy przedstawiono dolne ograniczenie na liczbę dominowania totalnego zewnętrznie spójnego w grafach oraz scharakteryzowano wszystkie drzewa osiągające to ograniczenie.
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Some variations of perfect graphs
PublicationWe consider (ψk−γk−1)-perfect graphs, i.e., graphs G for which ψk(H) =γk−1(H) for any induced subgraph H of G, where ψk and γk−1 are the k -path vertex cover number and the distance (k−1)-domination number, respectively. We study (ψk−γk−1)-perfect paths, cycles and complete graphs for k≥2. Moreover, we provide a complete characterisation of (ψ2−γ1)-perfect graphs describing the set of its forbidden induced subgraphs and providing...
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Convex universal fixers
PublicationPraca dotyczy dominowania wypukłego w grafach pryzmowych.