On saturation numbers of complete multipartite graphs and even cycles
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909646077296640 |
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| author | Mohammadian, Ali Poursoltani, Milad Tayfeh-Rezaie, Behruz |
| author_facet | Mohammadian, Ali Poursoltani, Milad Tayfeh-Rezaie, Behruz |
| contents | Given positive integer $n$ and graph $F$, the saturation number $\mathrm{sat}(n, F)$ is the minimum number of edges in an edge-maximal $F$-free graph on $n$ vertices. In this paper, we determine asymptotic behavior of $\mathrm{sat}(n, F)$ when $F$ is either a complete multipartite graph or a cycle graph whose length is even and large enough. This extends a result by Bohman, Fonoberova, and Pikhurko from 2010 as well as partially resolves a conjecture of Füredi and Kim from 2013. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_09767 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On saturation numbers of complete multipartite graphs and even cycles Mohammadian, Ali Poursoltani, Milad Tayfeh-Rezaie, Behruz Combinatorics 05C35, 05C38 Given positive integer $n$ and graph $F$, the saturation number $\mathrm{sat}(n, F)$ is the minimum number of edges in an edge-maximal $F$-free graph on $n$ vertices. In this paper, we determine asymptotic behavior of $\mathrm{sat}(n, F)$ when $F$ is either a complete multipartite graph or a cycle graph whose length is even and large enough. This extends a result by Bohman, Fonoberova, and Pikhurko from 2010 as well as partially resolves a conjecture of Füredi and Kim from 2013. |
| title | On saturation numbers of complete multipartite graphs and even cycles |
| topic | Combinatorics 05C35, 05C38 |
| url | https://arxiv.org/abs/2506.09767 |