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 in | Discrete Applied Mathematics Vol. 356; pp. 343 - 349 |
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Main Authors | , |
Format | Journal Article |
Language | English |
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Elsevier B.V
30.10.2024
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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. |
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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 |
Author_xml | – sequence: 1 givenname: Jia-Bao surname: Yang fullname: Yang, Jia-Bao – sequence: 2 givenname: Long-Tu surname: Yuan fullname: Yuan, Long-Tu email: ltyuan@math.ecnu.edu.cn |
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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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References | Lovász, Plummer (b9) 1986 Edmonds (b2) 1965; 17 Füredi, Kostochka, Luo, Verstraëte (b4) 2018; 341 Kopylov (b8) 1977; 18 Ma, Ning (b11) 2020; 40 Füredi, Kostochka, Verstraëte (b5) 2016; 121 Luo (b10) 2018; 128 J. Ma, L. Yuan, A clique version of the Erdős-Gallai stability theorems, submitted to SIAM J. Discrete Math. Ma, Yuan (b13) 2024; 38 Gallai (b7) 1964; 9 Erdős, Gallai (b3) 1959; 10 Wang (b14) 2020; 85 Gallai (b6) 1963; 8 Duan, Ning, Peng, Wang, Yang (b1) 2020; 287 Kopylov (10.1016/j.dam.2024.05.039_b8) 1977; 18 Füredi (10.1016/j.dam.2024.05.039_b4) 2018; 341 Gallai (10.1016/j.dam.2024.05.039_b7) 1964; 9 Füredi (10.1016/j.dam.2024.05.039_b5) 2016; 121 Ma (10.1016/j.dam.2024.05.039_b11) 2020; 40 10.1016/j.dam.2024.05.039_b12 Wang (10.1016/j.dam.2024.05.039_b14) 2020; 85 Gallai (10.1016/j.dam.2024.05.039_b6) 1963; 8 Edmonds (10.1016/j.dam.2024.05.039_b2) 1965; 17 Lovász (10.1016/j.dam.2024.05.039_b9) 1986 Ma (10.1016/j.dam.2024.05.039_b13) 2024; 38 Duan (10.1016/j.dam.2024.05.039_b1) 2020; 287 Erdős (10.1016/j.dam.2024.05.039_b3) 1959; 10 Luo (10.1016/j.dam.2024.05.039_b10) 2018; 128 |
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Kőzl. contributor: fullname: Gallai – volume: 38 start-page: 1757 issue: 2 year: 2024 ident: 10.1016/j.dam.2024.05.039_b13 article-title: A stability result of the Pósa lemma publication-title: SIAM J. Discrete Math. doi: 10.1137/20M1382143 contributor: fullname: Ma – volume: 85 year: 2020 ident: 10.1016/j.dam.2024.05.039_b14 article-title: The shifting method and generalized Turán number of matching publication-title: European J. Combin. doi: 10.1016/j.ejc.2019.103057 contributor: fullname: Wang – volume: 9 start-page: 401 year: 1964 ident: 10.1016/j.dam.2024.05.039_b7 article-title: Maximale systeme unabhängiger kanten publication-title: Magyar Tud. Akad. Mat. Kutató Int. Kőzl. contributor: fullname: Gallai – volume: 18 start-page: 593 year: 1977 ident: 10.1016/j.dam.2024.05.039_b8 article-title: On maximal paths and cycles in a graph publication-title: Soviet Math. 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Hungar. doi: 10.1007/BF02024498 contributor: fullname: Erdős – volume: 121 start-page: 197 year: 2016 ident: 10.1016/j.dam.2024.05.039_b5 article-title: Stability in the Erdős-Gallai theorem on cycles and paths publication-title: J. Combin. Theory Ser. B doi: 10.1016/j.jctb.2016.06.004 contributor: fullname: Füredi |
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Title | A note on the stability results of the number of cliques in graphs with given matching number |
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