Browsing Mathematics (Faculty of) by Author "MacDonald, Colter"
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On Finding Large Cliques when the Chromatic Number is close to the Maximum Degree
MacDonald, Colter (University of Waterloo, 2021-12-23)We prove that every graph G with chromatic number χ(G) = ∆(G) − 1 and ∆(G) ≥ 66 contains a clique of size ∆(G) − 17. Our proof closely parallels a proof from Cranston and Rabern, who showed that graphs with χ = ∆ and ∆ ≥ ...