On the Erdös-Lovász Tihany Conjecture for Claw-Free Graphs
نویسندگان
چکیده
In 1968, Erdös and Lovász conjectured that for every graph G and all integers s, t ≥ 2 such that s + t − 1 = χ(G) > ω(G), there exists a partition (S, T ) of the vertex set of G such that χ(G|S) ≥ s and χ(G|T ) ≥ t. For general graphs, the only settled cases of the conjecture are when s and t are small. Recently, the conjecture was proved for a few special classes of graphs: graphs with stability number 2 [1], line graphs [9] and quasi-line graphs [1]. In this paper, we consider the conjecture for claw-free graphs and present some progress on it.
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