E-resources
Peer reviewed
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Xu, Yian
Applied mathematics and computation, 01/2024, Volume: 461Journal Article
We use P5 to denote a path of length 5 and C5 to denote a cycle of length 5. The aim of this paper is to prove that, if G is a connected graph satisfying (1). G has an induced C5 and no clique cut-set, (2). G has no induced subgraph isomorphic to P5 or K5−e, then G is max{13,ω(G)+1}-colorable. •If a non-bipartite (P5,diamond)-free graph is not a complete graph or a 5-ring, then it contains an induced paw.•Let G be a (P5,K5−e)-free graph with an induced 5-cycle C. If G has an induced T-5-wheel Σ, then χ(G)≤max{13,ω(G)+1}.•Let G be (P5,K5−e)-free with an induced C5. Then χ(G)≤max{13,ω(G)+1}.
