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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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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Abstract 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.
AbstractList 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.
Author Yang, Jia-Bao
Yuan, Long-Tu
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Cites_doi 10.1016/j.jctb.2017.08.005
10.1137/20M1382143
10.1016/j.ejc.2019.103057
10.1007/s00493-019-3843-4
10.4153/CJM-1965-045-4
10.1016/j.disc.2017.12.018
10.1016/j.dam.2020.08.001
10.1007/BF02024498
10.1016/j.jctb.2016.06.004
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Keywords Clique
Matchings
Stability
Gallai–Edmonds theorem
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Snippet 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...
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StartPage 343
SubjectTerms Clique
Gallai–Edmonds theorem
Matchings
Stability
Title A note on the stability results of the number of cliques in graphs with given matching number
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