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Search results for: BIPARTITE GRAPH
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On the complexity of distributed graph coloring with local minimality constraints
PublicationArtykuł traktuje o zachłannym kolorowaniu grafów w modelu rozproszonym. Omówiono algorytmy rozproszone, dające w wyniku pokolorowanie spełniające warunki dla pokolorowań sekwencyjnych typu S oraz Largest-First (LF). Udowodniono również, że każda rozproszona implementacja algorytmu S wymaga co najmniej Omega(log n / log log n) rund, a algorytmu LF co najmniej Omega (n^{1/2}) rund, gdzie n oznacza liczbę wierzchołków grafu.
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Nordhaus-Gaddum results for the convex domination number of a graph
PublicationPraca dotyczy nierówności typu Nordhausa-Gadduma dla dominowania wypukłego.
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Constructing a map of an anonymous graph: applications of universal sequences
PublicationWe study the problem of mapping an unknown environmentrepresented as an unlabelled undirected graph. A robot (or automaton)starting at a single vertex of the graph G has to traverse the graph and return to its starting point building a map of the graph in the process. We are interested in the cost of achieving this task (whenever possible) in terms of the number of edge traversal made by the robot. Another optimization criteria...
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Scheduling with Complete Multipartite Incompatibility Graph on Parallel Machines
PublicationIn this paper we consider a problem of job scheduling on parallel machines with a presence of incompatibilities between jobs. The incompatibility relation can be modeled as a complete multipartite graph in which each edge denotes a pair of jobs that cannot be scheduled on the same machine. Our research stems from the works of Bodlaender, Jansen, and Woeginger (1994) and Bodlaender and Jansen (1993). In particular, we pursue the...
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Graph Representation Integrating Signals for Emotion Recognition and Analysis
PublicationData reusability is an important feature of current research, just in every field of science. Modern research in Affective Computing, often rely on datasets containing experiments-originated data such as biosignals, video clips, or images. Moreover, conducting experiments with a vast number of participants to build datasets for Affective Computing research is time-consuming and expensive. Therefore, it is extremely important to...
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On Tradeoffs Between Width- and Fill-like Graph Parameters
PublicationIn 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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Dataset of non-isomorphic graphs being coloring types (K4-e,Km-e;n), 2<m<7, 1<n<R(K4-e,Km-e)
Open Research DataFor 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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Classical coloring of graphs.
PublicationRozdział obejmuje klasyczne kolorowanie krawędzi i wierzołków w grafach prostych. Oprócz podstawowych definicji podane zostały najczęściej stosowane metody przybliżone oraz ich właściwości. Dodatkowo rozdział zawiera przegląd znanych benczmarków dla podanych metod w kontekście klasycznego modelu kolorowania.
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Sum Coloring of Graphs.
PublicationRozdział jest poświęcony sumacyjnemu kolorowaniu grafów. Przedstawiono jego podstawowe własności oraz zastosowania praktyczne.
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Rank Coloring of Graphs.
PublicationRozdział jest poświęcony uporządkowanemu kolorowaniu grafów. Przedstawiono jego podstawowe własności oraz zastosowania praktyczne.
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Circular colorings of graphs.
PublicationRozdział poświęcony jest cyrkularnemu modelowi kolorowania krawędzi. Rozważana jest zarówno wersja wierzchołkowa i krawędziowa. Szczególny nacisk położono na złożoność obliczeniową i zastosowania dla omawianych modeli kolorowania.
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T-coloring of graphs.
PublicationNiniejszy rozdział omawia kontrastowe kolorowanie grafów. Podana została jego definicja i podstawowe własności, zastosowania oraz złożoność obliczeniowa problemów rozważanych w ramach tej dziedziny.
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Harmonions Coloring of Graphs.
PublicationProblem kolorowania grafów jest motywowany radionawigacją lotniczą, kompresją obrazów i in. W rozdziale podano podstawowe fakty dotyczące tego modelu kolorowania, a wsród nich dolne i górne oszacowania na liczbę harmoniczną i algorytm o złożoności 0 (mm3) dający bardzo dobre pokolorowania przybliżone.
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Strategic balance in graphs
PublicationFor a given graph G, a nonempty subset S contained in V ( G ) is an alliance iff for each vertex v ∈ S there are at least as many vertices from the closed neighbourhood of v in S as in V ( G ) − S. An alliance is global if it is also a dominating set of G. The alliance partition number of G was defined in Hedetniemi et al. (2004) to be the maximum number of sets in a partition of V ( G ) such that each set is an alliance. Similarly,...
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Named Property Graphs
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Serialization for Property Graphs
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2-bondage in graphs
PublicationA 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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Double bondage in graphs
PublicationA 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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Dynamic coloring of graphs
PublicationDynamics is an inherent feature of many real life systems so it is natural to define and investigate the properties of models that reflect their dynamic nature. Dynamic graph colorings can be naturally applied in system modeling, e.g. for scheduling threads of parallel programs, time sharing in wireless networks, session scheduling in high-speed LAN's, channel assignment in WDM optical networks as well as traffic scheduling. In...
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Common Independence in Graphs
PublicationAbstract: The cardinality of a largest independent set of G, denoted by α(G), is called the independence number of G. The independent domination number i(G) of a graph G is the cardinality of a smallest independent dominating set of G. We introduce the concept of the common independence number of a graph G, denoted by αc(G), as the greatest integer r such that every vertex of G belongs to some independent subset X of VG with |X|...
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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)
Open Research DataFor 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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Paired domination versus domination and packing number in graphs
PublicationGiven a graph G = (V(G), E(G)), the size of a minimum dominating set, minimum paired dominating set, and a minimum total dominating set of a graph G are denoted by γ (G), γpr(G), and γt(G), respectively. For a positive integer k, a k-packing in G is a set S ⊆ V(G) such that for every pair of distinct vertices u and v in S, the distance between u and v is at least k + 1. The k-packing number is the order of a largest kpacking and...
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Similarities and Differences Between the Vertex Cover Number and the Weakly Connected Domination Number of a Graph
PublicationA vertex cover of a graph G = (V, E) is a set X ⊂ V such that each edge of G is incident to at least one vertex of X. The ve cardinality of a vertex cover of G. A dominating set D ⊆ V is a weakly connected dominating set of G if the subgraph G[D]w = (N[D], Ew) weakly induced by D, is connected, where Ew is the set of all edges having at least one vertex in D. The weakly connected domination number γw(G) of G is the minimum cardinality...
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Equitable coloring of corona products of graphs
PublicationIn 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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ON THE NON-LOCALITY OF TRIPARTITE NON-SINGALING BOXES EMERGING FROM WIRINGS
PublicationIt has been recently shown, that some of the tripartite boxes admittin g bilocal decom- position, lead to non-locality under wiring operation applied to t wo of the subsystems [R. Gallego et al. Physical Review Letters 109 , 070401 (2012)]. In the following, we study this phenomenon quantitatively. Basing on the known classes of bo xes closed un- der wirings, we introduce multipartite monotones which are count erparts of bipartite ones...
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Neural Graph Collaborative Filtering: Analysis of Possibilities on Diverse Datasets
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Tighter bounds on the size of a maximum P3-matching in a cubic graph
PublicationW pracy pokazano, że największe P3-skojarzenie dla dowolnego grafu o n>16 wierzchołkach składa się z przynajmniej 117n/152 wierzchołków.
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Modelling of energy flow in mechatronic systems. A bond graph approach
PublicationW referacie przedstawiono w sposób jednoliy modelowanie systemów mechatroniki metodą grafów wiązań (GW) w aspekcie symulacji przepływu energii. Omówiono ogólne założenia modelowania w ujęciu GW. Modelowanie przepływu energii rozważano na przykładzie napędu pojazdu hybrydowego PH-MAK.
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Towards explainable motion prediction using heterogeneous graph representations
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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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Modelling of energy flow in electrical machines. A bond graph approach
PublicationPrzedstawiono w ujęcia grafów wiązań model przepływu energii/mocy w maszynach elektrycznych pracujących w hybrydowych systemach przetwarzania energii. Jako przykład do rozważań przyjęto system napędu trakcyjnego pojazdów hybrydowych.
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Comparison of reproduction strategies in genetic algorithm approach to graph searching
Publicationgenetic algorithms (ga) are a well-known tool used to obtain approximate solutions to optimization problems. successful application of genetic algorithm in solving given problem is largely dependant on selecting appropriate genetic operators. selection, mutation and crossover techniques play a fundamental role in both time needed to obtain results and their accuracy. in this paper we focus on applying genetic algorithms in calculating...
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Self-stabilizing algorithms for graph coloring with improved performance guarantees
PublicationW pracy rozważa się rozproszony model obliczeń, w którym struktura systemu jest reprezentowana przez graf bezpośrednich połączeń komunikacyjnych. W tym modelu podajemy nowy samostabilizujący algorytm kolorowania grafów oparty na konstrukcji drzewa spinającego. Zgodnie z naszą wiedzą jest to pierwszy algorytm z gwarantowaną wielomianową liczbą ruchów, który dokładnie koloruje grafy dwudzielne.
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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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Neural Graph Collaborative Filtering: Analysis of Possibilities on Diverse Datasets
PublicationThis paper continues the work by Wang et al. [17]. Its goal is to verify the robustness of the NGCF (Neural Graph Collaborative Filtering) technique by assessing its ability to generalize across different datasets. To achieve this, we first replicated the experiments conducted by Wang et al. [17] to ensure that their replication package is functional. We received sligthly better results for ndcg@20 and somewhat poorer results for...
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2-Coloring number revisited
Publication2-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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A 27/26-approximation algorithm for the chromatic sum coloring of bipartitegraphs
PublicationWe consider the CHROMATIC SUM PROBLEM on bipartite graphs which appears to be much harder than the classical CHROMATIC NUMBER PROBLEM. We prove that the CHROMATIC SUM PROBLEM is NP-complete on planar bipartite graphs with Delta less than or equal to 5, but polynomial on bipartite graphs with Delta less than or equal to 3, for which we construct an O(n(2))-time algorithm. Hence, we tighten the borderline of intractability for this...
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Greedy T-colorings of graphs
PublicationTreścią artykułu są pokolorowania kontrastowe wygenerowane przez algorytm zachłanny. Zbadane zostały ich własności, obejmujące liczbę kolororów, rozpiętość i rozpiętość krawędziową.
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Interval Edge-Coloring of Graphs
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Path Coloring and Routing in Graphs.
PublicationW rozdziale omówione zostały problemy kolorowania ścieżek i routingu w grafach. Podano podstawowe definicje związane z tymi problemami, znane wyniki wraz z dyskusją złożoności obliczeniowej dla grafów ogólnych i dla kilku podstawowych klas grafów oraz zastosowania.
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Interval edge-coloring of graphs.
PublicationRozdział poświęcony prezentacji modelu zwartego kolorowania krawędziowego grafów i jego znanych własności. Szczególny nacisk położono na opis klas grafów dających się pokolorować zwarcie w czasie wielomianowym. Omówiono także stratność jako miarę niepodatności grafu na kolorowanie zwarte.
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Global defensive sets in graphs
PublicationIn the paper we study a new problem of finding a minimum global defensive set in a graph which is a generalization of the global alliance problem. For a given graph G and a subset S of a vertex set of G, we define for every subset X of S the predicate SEC ( X ) = true if and only if | N [ X ] ∩ S | ≥ | N [ X ] \ S | holds, where N [ X ] is a closed neighbourhood of X in graph G. A set S is a defensive alliance if and only if for...
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Correction to: Serialization for Property Graphs
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Three-fast-searchable graphs
PublicationIn the edge searching problem, searchers move from vertex to vertex in a graph to capture an invisible, fast intruder that may occupy either vertices or edges. Fast searching is a monotonic internal model in which, at every move, a new edge of the graph G must be guaranteed to be free of the intruder. That is, once all searchers are placed the graph G is cleared in exactly |E(G)| moves. Such a restriction obviously necessitates...
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On-line ranking of split graphs
PublicationA vertex ranking of a graph G is an assignment of positive integers (colors) to the vertices of G such that each path connecting two vertices of the same color contains a vertex of a higher color. Our main goal is to find a vertex ranking using as few colors as possible. Considering on-line algorithms for vertex ranking of split graphs, we prove that the worst case ratio of the number of colors used by any on-line ranking algorithm...
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Deterministic Rendezvous in Restricted Graphs
PublicationIn this paper we consider the problem of synchronous rendezvous in which two anonymous mobile entities (robots) A and B are expected to meet at the same time and point in a graph G = (V;E). Most of the work devoted to rendezvous in graphs assumes that robots have access to the same sets of nodes and edges, where the topology of connections may be initially known or unknown. In our work we assume the movement of robots is restricted...
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Algorithms for testing security in graphs
PublicationIn this paper we propose new algorithmic methods giving with the high probability the correct answer to the decision problem of security in graphs. For a given graph G and a subset S of a vertex set of G we have to decide whether S is secure, i.e. every subset X of S fulfils the condition: |N[X] \cap S| >= |N[X] \ S|, where N[X] is a closed neighbourhood of X in graph G. We constructed a polynomial time property pseudotester based...
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Bondage number of grid graphs
PublicationThe bondage number b(G) of a nonempty graph G is the cardinality of a smallest set of edges whose removal from G results in a graph with domination number greater than the domination number of G. Here we study the bondage number of some grid-like graphs. In this sense, we obtain some bounds or exact values of the bondage number of some strong product and direct product of two paths.
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Super Dominating Sets in Graphs
PublicationIn this paper some results on the super domination number are obtained. We prove that if T is a tree with at least three vertices, then n2≤γsp(T)≤n−s, where s is the number of support vertices in T and we characterize the extremal trees.
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A note on total reinforcement in graphs
PublicationIn this note we prove a conjecture and inprove some results presendet in a recent paper of N. Sridharan, M.D. Elias, V.S.A. Subramanian, Total reinforcement number of a graph, AKCE Int. J. Graphs Comb. 4 (2) (2007) 197-202.