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arXiv · 2404.11268

The maximum number of cliques in graphs with given fractional matching number and minimum degree

Chengli Li·Yurui Tang
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Abstract

Recently, Ma, Qian and Shi determined the maximum size of an $n$-vertex graph with given fractional matching number $s$ and maximum degree at most $d$. Motivated by this result, we determine the maximum number of $\ell$-cliques in a graph with given fractional matching number and minimum degree, which generalizes Shi and Ma's result about the maximum size of a graph with given fractional matching number and minimum degree at least one. We also determine the maximum number of complete bipartite graphs in a graph with prescribed fractional matching number and minimum degree.

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Chengli Li, Yurui Tang. 2024-04-17. The maximum number of cliques in graphs with given fractional matching number and minimum degree. https://arxiv.org/abs/2404.11268

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