Counting cliques in 1-planar graphs

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...

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Bibliographic Details
Published inEuropean journal of combinatorics Vol. 109; p. 103654
Main Authors Gollin, J. Pascal, Hendrey, Kevin, Methuku, Abhishek, Tompkins, Casey, Zhang, Xin
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.03.2023
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Summary: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.
ISSN:0195-6698
1095-9971
DOI:10.1016/j.ejc.2022.103654