A stability theorem for multi-partite graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866918286470414336 |
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| author | Chen, Wanfang Lu, Changhong Yuan, Long-Tu |
| author_facet | Chen, Wanfang Lu, Changhong Yuan, Long-Tu |
| contents | The Erdős-Simonovits stability theorem is one of the most widely used theorems in extremal graph theory. We obtain an Erdős-Simonovits type stability theorem in multi-partite graphs. Different from the Erdős-Simonovits stability theorem, our stability theorem in multi-partite graphs says that if the number of edges of an $H$-free graph $G$ is close to the extremal graphs for $H$, then $G$ has a well-defined structure but may be far away to the extremal graphs for $H$. As an application, we solve a conjecture posed by Han and Zhao concerning the maximum number of edges in multi-partite graphs which does not contain vertex-disjoint copies of a clique |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_13995 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A stability theorem for multi-partite graphs Chen, Wanfang Lu, Changhong Yuan, Long-Tu Combinatorics The Erdős-Simonovits stability theorem is one of the most widely used theorems in extremal graph theory. We obtain an Erdős-Simonovits type stability theorem in multi-partite graphs. Different from the Erdős-Simonovits stability theorem, our stability theorem in multi-partite graphs says that if the number of edges of an $H$-free graph $G$ is close to the extremal graphs for $H$, then $G$ has a well-defined structure but may be far away to the extremal graphs for $H$. As an application, we solve a conjecture posed by Han and Zhao concerning the maximum number of edges in multi-partite graphs which does not contain vertex-disjoint copies of a clique |
| title | A stability theorem for multi-partite graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2208.13995 |