The maximum number of cliques in graphs with given fractional matching number and minimum degree
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910413584596992 |
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| author | Li, Chengli Tang, Yurui |
| author_facet | Li, Chengli Tang, Yurui |
| contents | Recently, Ma, Qian and Shi determined the maximum size of an $n$-vertex graph with given fractional matching number $s$ and maximum degree at most $d$. Motivated by this result, we determine the maximum number of $\ell$-cliques in a graph with given fractional matching number and minimum degree, which generalizes Shi and Ma's result about the maximum size of a graph with given fractional matching number and minimum degree at least one. We also determine the maximum number of complete bipartite graphs in a graph with prescribed fractional matching number and minimum degree. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11268 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The maximum number of cliques in graphs with given fractional matching number and minimum degree Li, Chengli Tang, Yurui Combinatorics Recently, Ma, Qian and Shi determined the maximum size of an $n$-vertex graph with given fractional matching number $s$ and maximum degree at most $d$. Motivated by this result, we determine the maximum number of $\ell$-cliques in a graph with given fractional matching number and minimum degree, which generalizes Shi and Ma's result about the maximum size of a graph with given fractional matching number and minimum degree at least one. We also determine the maximum number of complete bipartite graphs in a graph with prescribed fractional matching number and minimum degree. |
| title | The maximum number of cliques in graphs with given fractional matching number and minimum degree |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2404.11268 |