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arXiv · 2109.02906

Counting cliques in $1$-planar graphs

J. Pascal Gollin·Kevin Hendrey·Abhishek Methuku·Casey Tompkins·Xin Zhang
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Abstract

The problem of maximising the number of cliques among $n$-vertex graphs from various graph classes has received considerable attention. We investigate this problem for the class of $1$-planar graphs where we determine precisely the maximum total number of cliques as well as the maximum number of cliques of any fixed size. We also precisely characterise the extremal graphs for these problems.

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J. Pascal Gollin, Kevin Hendrey, Abhishek Methuku, Casey Tompkins, Xin Zhang. 2021-09-07. Counting cliques in $1$-planar graphs. https://arxiv.org/abs/2109.02906

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