Structural domination and coloring of some (P7,C7)-free graphs

Article Type

Research Article

Publication Title

Discrete Mathematics


We show that every connected induced subgraph of a graph G is dominated by an induced connected split graph if and only if G is C-free, where C is a set of six graphs which includes P7 and C7, and each containing an induced P5. A similar characterization is shown for the class of graphs which are dominated by an induced connected complete split graph. Motivated by these results, we study structural descriptions of some classes of (P7, C7)-free graphs. In particular, we give structural descriptions for the class of (P7, C7, C4, gem)-free graphs and for the class of (P7, C7, C4, diamond)-free graphs. Using these results, we show that every (P7, C7, C4, gem)-free graph G satisfies χ(G)≤2ω(G)−1, and that every (P7, C7, C4, diamond)-free graph H satisfies χ(H)≤max{3,ω(H)}.



Publication Date



Open Access, Green

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