Results 81 to 90 of about 258 (128)
Edge Colouring Reduced Indifference Graphs
, 1999 The chromatic index problem -- finding the minimum number of colours required for colouring the edges of a graph -- is still unsolved for indifference graphs, whose vertices can be linearly ordered so that the vertices contained in the same maximal ...
Celina M. H. De Figueiredo +3 more
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Distinguishing Cartesian Products of Countable Graphs
Discussiones Mathematicae Graph Theory, 2017 The distinguishing number D(G) of a graph G is the minimum number of colors needed to color the vertices of G such that the coloring is preserved only by the trivial automorphism.
Estaji Ehsan +4 more
doaj +1 more source
Rainbow Connection Number of Graphs with Diameter 3
Discussiones Mathematicae Graph Theory, 2017 A path in an edge-colored graph G is rainbow if no two edges of the path are colored the same. The rainbow connection number rc(G) of G is the smallest integer k for which there exists a k-edge-coloring of G such that every pair of distinct vertices of G
Li Hengzhe, Li Xueliang, Sun Yuefang
doaj +1 more source
Bounds for partial list colourings
, 2008 : Let G be a simple graph on n vertices with list chromatic number χ l = s. If each vertex of G is assigned a list of t colours Albertson, Grossman and Haas [1] asked how many of the vertices, λ t,s, are necessarily colourable from these lists?
D. Hanson, G. Macgillivray, R. Haas
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Decomposition of bounded degree graphs into C4-free subgraphs
We prove that every graph with maximum degree ∆ admits a partition of its edges into O(√∆) parts (as ∆→∞) none of which contains C4 as a subgraph. This bound is sharp up to a constantfactor. Our proof uses an iterated random colouring procedure.Keywords:
Kang, Ross, Perarnau Llobet, Guillem
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Almost All Graphs With 2.522n Edges Are Not 3-Colorable
, 1999 We prove that for c 2:522 a random graph with n vertices and m = cn edges is not 3-colorable with probability 1 \Gamma o(1). Similar bounds for non-k-colorability are given for k ? 3.
Achlioptas, D. +3 more
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Local Conditions for Edge-Coloring
, 1995 In this note, we investigate three versions of the overfull property for graphs and their relation to the edge-coloring problem. Each of these properties implies that the graph cannot be edge-colored with \Delta colors, where \Delta is the maximum degree.
Celina M. H. De Figueiredo +2 more
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List Edge Colourings of Some 1-Factorable Multigraphs
, 1996 The List Edge Colouring Conjecture asserts that, given any multigraph G with chromatic index k and any set system fSe : e 2 E(G)g with each jSe j = k, we can choose elements se 2 Se such that se 6= sf whenever e and f are adjacent edges.
Luis Goddyn, M. N. Ellingham
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Some Results on the Structure of Multipoles in the Study of Snarks ∗
, 2014 AMS classification: 05C15, 05C05, 05C38. Multipoles are the pieces we obtain by cutting some edges of a cubic graph. As a result of the cut, a multipole M has dangling edges with one free end, which we call semiedges.
J. Vilaltella, M. A. Fiol
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Game Chromatic Number of Graphs
, 1998 We show that if a graph has acyclic chromatic number k, then its game chromatic number is at most k(k + 1). By applying the known upper bounds for the acyclic chromatic numbers of various classes of graphs, we obtain upper bounds for the game chromatic ...
Xuding Zhu, Thomas Dinski
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