Bounding χ in terms of ω and ∆ for quasi-line graphs
نویسنده
چکیده
A quasi-line graph is a graph in which the neighbourhood of any vertex can be covered by two cliques; every line graph is a quasi-line graph. Reed conjectured that for any graph G, χ(G) ≤ d12(∆(G) + 1 + ω(G))e [13]. We prove that the conjecture holds if G is a quasi-line graph, extending a result of King, Reed and Vetta, who proved the conjecture for line graphs [8], and improving the bound of χ(G) ≤ 32ω(G) given by Chudnovsky and Ovetsky [2].
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