# The chromatic number of (P_5, HVN )-free graphs

@inproceedings{Xu2022TheCN, title={The chromatic number of (P\_5, HVN )-free graphs}, author={Yian Xu}, year={2022} }

Let G be a graph. We use χ ( G ) and ω ( G ) to denote the chromatic number and clique number of G respectively. A P 5 is a path on 5 vertices, and an HV N is a K 4 together with one more vertex which is adjacent to exactly two vertices of K 4 . In this paper, we show that if G is ( P 5 , HVN )-free, then χ ( G ) ≤ ω ( G ) + 3. This generalizes some results on χ -bounded problem of P 5 -free graphs, and this upper bound is almost sharp as there are many ( P 5 , K 4 )-free graphs with chromatic…

## 7 Citations

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