منابع مشابه
Colouring Diamond-free Graphs
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A vertex colouring assigns to each vertex of a graph a colour such that adjacent vertices have different colours. The algorithmic complexity of the Colouring problem, asking for the smallest number of colours needed to vertex-colour a given graph, is known for a large number of graph classes. Notably it is NP-complete in general, but polynomial time solvable for perfect graphs. A triple of vert...
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In this paper we prove that if G is a connected claw-free graph with three pairwise non-adjacent vertices, with chromatic number χ and clique number ω, then χ ≤ 2ω and the same for the complement of G. We also prove that the choice number of G is at most 2ω, except possibly in the case when G can be obtained from a subgraph of the Schläfli graph by replicating vertices. Finally, we show that th...
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Is there some absolute ε > 0 such that for any claw-free graph G, the chromatic number of the square of G satisfies χ(G) ≤ (2−ε)ω(G), where ω(G) is the clique number of G? Erdős and Nešetřil asked this question for the specific case of G the line graph of a simple graph and this was answered in the affirmative by Molloy and Reed. We show that the answer to the more general question is also yes,...
متن کاملColouring of ( P3 ∪ P2)-free graphs
The class of 2K2-free graphs and its various subclasses have been studied in a variety of contexts. In this paper, we are concerned with the colouring of (P3 ∪P2)-free graphs, a super class of 2K2-free graphs. We derive a O(ω3) upper bound for the chromatic number of (P3 ∪P2)-free graphs, and sharper bounds for (P3 ∪P2, diamond)-free graphs, where ω denotes the clique number. By applying simila...
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ژورنال
عنوان ژورنال: Algorithmica
سال: 2020
ISSN: 0178-4617,1432-0541
DOI: 10.1007/s00453-020-00675-w