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arXiv · 1511.04655

Cliques in Graphs Excluding a Complete Graph Minor

David R. Wood
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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 $t\leq 9$ 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 $t\leq 9$. Several observations are made about the case of general $t$.

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David R. Wood. 2016-07-15. Cliques in Graphs Excluding a Complete Graph Minor. https://arxiv.org/abs/1511.04655

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