Search results for "Clique-sum"

showing 3 items of 3 documents

Neighbor-Distinguishing k-tuple Edge-Colorings of Graphs

2009

AbstractThis paper studies proper k-tuple edge-colorings of graphs that distinguish neighboring vertices by their sets of colors. Minimum numbers of colors for such colorings are determined for cycles, complete graphs and complete bipartite graphs. A variation in which the color sets assigned to edges have to form cyclic intervals is also studied and similar results are given.

Circular coloringComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION0102 computer and information sciences[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]01 natural sciencesGraphTheoretical Computer ScienceCombinatoricsGreedy coloringIndifference graphChordal graphDiscrete Mathematics and Combinatorics0101 mathematicsFractional coloringComputingMilieux_MISCELLANEOUSComputingMethodologies_COMPUTERGRAPHICSMathematicsDiscrete mathematicsk-tuple edge-coloringClique-sum010102 general mathematics[ INFO.INFO-DM ] Computer Science [cs]/Discrete Mathematics [cs.DM]1-planar graphMetric dimension010201 computation theory & mathematicsIndependent setMaximal independent setNeighbor-distinguishingMathematicsofComputing_DISCRETEMATHEMATICSAdjacent vertex-distinguishing
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On the chromatic number of disk graphs

1998

Colorings of disk graphs arise in the study of the frequency-assignment problem in broadcast networks. Motivated by the observations that the chromatic number of graphs modeling real networks hardly exceeds their clique number, we examine the related properties of the unit disk (UD) graphs and their different generalizations. For all these graphs including the most general class of the double disk (DD) graphs, it is shown that X(G) ≤ c.ω(G) for a constant c. Several coloring algorithms are analyzed for disk graphs, aiming to improve the bounds on X(G). We find that their worst-case performance expressed in the number of used colors is indeed reached in some instances.

Clique-sumComputer Networks and CommunicationsTrapezoid graph1-planar graphMetric dimensionCombinatoricsIndifference graphPathwidthHardware and ArchitectureChordal graphMaximal independent setSoftwareMathematicsofComputing_DISCRETEMATHEMATICSInformation SystemsMathematicsNetworks
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Some properties of vertex-oblique graphs

2016

The type t G ( v ) of a vertex v ? V ( G ) is the ordered degree-sequence ( d 1 , ? , d d G ( v ) ) of the vertices adjacent with v , where d 1 ? ? ? d d G ( v ) . A graph G is called vertex-oblique if it contains no two vertices of the same type. In this paper we show that for reals a , b the class of vertex-oblique graphs G for which | E ( G ) | ? a | V ( G ) | + b holds is finite when a ? 1 and infinite when a ? 2 . Apart from one missing interval, it solves the following problem posed by Schreyer et?al. (2007): How many graphs of bounded average degree are vertex-oblique? Furthermore we obtain the tight upper bound on the independence and clique numbers of vertex-oblique graphs as a fun…

Discrete mathematicsClique-sumNeighbourhood (graph theory)020206 networking & telecommunications0102 computer and information sciences02 engineering and technology01 natural sciencesTheoretical Computer ScienceMetric dimensionCombinatoricsIndifference graphNew digraph reconstruction conjecture010201 computation theory & mathematicsChordal graphIndependent set0202 electrical engineering electronic engineering information engineeringDiscrete Mathematics and CombinatoricsBound graphirregular graphsindependence numbervertex-oblique graphslexicographic productMathematicsDiscrete Mathematics
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