English

Counting cliques in $1$-planar graphs

Combinatorics 2021-09-08 v1

Abstract

The problem of maximising the number of cliques among nn-vertex graphs from various graph classes has received considerable attention. We investigate this problem for the class of 11-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.

Keywords

Cite

@article{arxiv.2109.02906,
  title  = {Counting cliques in $1$-planar graphs},
  author = {J. Pascal Gollin and Kevin Hendrey and Abhishek Methuku and Casey Tompkins and Xin Zhang},
  journal= {arXiv preprint arXiv:2109.02906},
  year   = {2021}
}

Comments

38 pages, 8 figures

R2 v1 2026-06-24T05:44:45.489Z