A note on the stability results of the number of cliques in graphs with given matching number

Duan, Ning, Peng, Wang and Yang determined the maximum number of s-cliques of a graph with given minimum degree and matching number. In this note, we prove a stability version of their theorem. Namely, we prove that if the number of s-cliques in a graph G is close to the above maximum number from th...

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Bibliographic Details
Published inDiscrete Applied Mathematics Vol. 356; pp. 343 - 349
Main Authors Yang, Jia-Bao, Yuan, Long-Tu
Format Journal Article
LanguageEnglish
Published Elsevier B.V 30.10.2024
Subjects
Clique
Gallai–Edmonds theorem
Matchings
Stability
Clique
Matchings
Stability
Gallai–Edmonds theorem
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Summary:Duan, Ning, Peng, Wang and Yang determined the maximum number of s-cliques of a graph with given minimum degree and matching number. In this note, we prove a stability version of their theorem. Namely, we prove that if the number of s-cliques in a graph G is close to the above maximum number from their theorem, then G must be a subgraph of some well-specified graphs.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2024.05.039