### Abstract

Let C be a clique covering for E(G) and let v be a vertex of G. The valency of vertex v (with respect to C), denoted by val_{C}(v), is the number of cliques in C containing v. The local clique cover number of G, denoted by lcc(G), is defined as the smallest integer k, for which there exists a clique covering for E(G) such that val_{C}(v) is at most k, for every vertex v∈V(G). In this paper, among other results, we prove that if G is a claw-free graph, then lcc(G)+χ(G)≤n+1.

Original language | English |
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Article number | 103114 |

Journal | European Journal of Combinatorics |

Volume | 88 |

DOIs | |

Publication status | Published - Aug 2020 |

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics

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## Cite this

Bujtás, C., Davoodi, A., Győri, E., & Tuza, Z. (2020). Clique coverings and claw-free graphs.

*European Journal of Combinatorics*,*88*, [103114]. https://doi.org/10.1016/j.ejc.2020.103114