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Coloring graphs with no induced five-vertex path or gem (1810.06186v2)
Published 15 Oct 2018 in math.CO and cs.DM
Abstract: For a graph $G$, let $\chi(G)$ and $\omega(G)$ respectively denote the chromatic number and clique number of $G$. We give an explicit structural description of ($P_5$,gem)-free graphs, and show that every such graph $G$ satisfies $\chi(G)\le \lceil\frac{5\omega(G)}{4}\rceil$. Moreover, this bound is best possible.
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