### Abstract

This paper considers the following question: What is the maximum number of k-cliques in an n-vertex graph with no K_{t}-minor? This question generalises the extremal function for K_{t}-minors, which corresponds to the k = 2 case. The exact answer is given for t ≤ 9 and all values of k. We also determine the maximum total number of cliques in an n-vertex graph with no K_{t}-minor for t ≤ 9. Several observations are made about the case of general t.

Original language | English |
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Article number | P3.18 |

Number of pages | 16 |

Journal | Electronic Journal of Combinatorics |

Volume | 23 |

Issue number | 3 |

Publication status | Published - 5 Aug 2016 |

### Keywords

- Clique
- Graph theory
- Minor

## Cite this

Wood, D. R. (2016). Cliques in graphs excluding a complete graph minor.

*Electronic Journal of Combinatorics*,*23*(3), [P3.18].