Graphs with χ=Δ Have Big Cliques
نویسندگان
چکیده
Brooks’ Theorem implies that if a graph has ∆ ≥ 3 and and χ > ∆, then ω = ∆+1. Borodin and Kostochka conjectured that if ∆ ≥ 9 and χ ≥ ∆, then ω ≥ ∆. We show that if ∆ ≥ 13 and χ ≥ ∆, then ω ≥ ∆ − 3. For a graph G, let H(G) denote the subgraph of G induced by vertices of degree ∆. We also show that if χ ≥ ∆, then ω ≥ ∆ or ω(H(G)) ≥ ∆− 5.
منابع مشابه
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ورودعنوان ژورنال:
- SIAM J. Discrete Math.
دوره 29 شماره
صفحات -
تاریخ انتشار 2015