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

Jia Bao Yang; Long Tu Yuan

doi:10.1016/j.dam.2024.05.039

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

Jia Bao Yang
, Long Tu Yuan^*

^*此作品的通讯作者

数学科学学院

East China Normal University

科研成果: 期刊稿件 › 文章 › 同行评审

1 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	343-349
页数	7
期刊	Discrete Applied Mathematics
卷	356
DOI	https://doi.org/10.1016/j.dam.2024.05.039
出版状态	已出版 - 30 10月 2024

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10.1016/j.dam.2024.05.039

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title = "A note on the stability results of the number of cliques in graphs with given matching number",

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.",

keywords = "Clique, Gallai–Edmonds theorem, Matchings, Stability",

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note = "Publisher Copyright: {\textcopyright} 2024",

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T1 - A note on the stability results of the number of cliques in graphs with given matching number

AU - Yang, Jia Bao

AU - Yuan, Long Tu

PY - 2024/10/30

Y1 - 2024/10/30

N2 - 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.

AB - 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.

KW - Clique

KW - Gallai–Edmonds theorem

KW - Matchings

KW - Stability

UR - https://www.scopus.com/pages/publications/85196946666

U2 - 10.1016/j.dam.2024.05.039

DO - 10.1016/j.dam.2024.05.039

M3 - 文章

AN - SCOPUS:85196946666

SN - 0166-218X

VL - 356

SP - 343

EP - 349

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

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

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