# On the chromatic number of a family of odd hole free graphs

@article{Song2021OnTC, title={On the chromatic number of a family of odd hole free graphs}, author={Jialei Song and Baogang Xu}, journal={ArXiv}, year={2021}, volume={abs/2110.12710} }

A hole is an induced cycle of length at least 4, and an odd hole is a hole of odd length. A full house is a graph composed by a vertex adjacent to both ends of an edge in K4. Let H be the complement of a cycle on 7 vertices. Chudnovsky et al [6] proved that every (odd hole, K4)-free graph is 4-colorable and is 3-colorable if it does not has H as an induced subgraph. In this paper, we use the proving technique of Chudnovsky et al to generalize this conclusion to (odd hole, full house)-free…

## One Citation

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

- Mathematics
- 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…

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