### Abstract

A diamond is a graph on four vertices with exactly one pair of nonadjacent vertices, and an odd hole is an induced cycle of odd length greater than 3. If G and H are graphs, G is H-free if no induced subgraph of G is isomorphic to H. A clique-coloring of G is an assignment of colors to the vertices of G such that no inclusion-wise maximal clique of size at least 2 is monochromatic. We show that every (diamond, odd-hole)-free graph is 3-clique-colorable, answering a question of Bacsó et al. (SIAM J Discrete Math 17(3) (2004), 361–376).

Original language | English (US) |
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Pages (from-to) | 5-41 |

Number of pages | 37 |

Journal | Journal of Graph Theory |

Volume | 86 |

Issue number | 1 |

DOIs | |

State | Published - Sep 2017 |

### All Science Journal Classification (ASJC) codes

- Geometry and Topology

### Keywords

- clique-coloring
- diamond-free
- odd-hole-free
- perfect graphs

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## Cite this

Chudnovsky, M., & Lo, I. (2017). Decomposing and Clique-Coloring (Diamond, Odd-Hole)-Free Graphs.

*Journal of Graph Theory*,*86*(1), 5-41. https://doi.org/10.1002/jgt.22110