Clique factors in random samplings of regular graphs
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915692605865984 |
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| author | Sun, Wanting Wei, Shunan Yang, Donglei |
| author_facet | Sun, Wanting Wei, Shunan Yang, Donglei |
| contents | We show that for any integer $r\ge 2$, there exists a constant $c>0$ such that for every sufficiently large integer $n$, every $((r-1)n+1)$-regular graph $G$ on $rn$ vertices has at least $c2^{rn}$ subsets $S\subseteq V(G)$ such that $G[S]$ contains a $K_r$-factor. This confirms a conjecture of Draganić, Keevash and Müyesser for large $n$ [Cyclic subsets in regular Dirac graphs. Int. Math. Res. Not., 2025(14): 1-16, 2025]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20287 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Clique factors in random samplings of regular graphs Sun, Wanting Wei, Shunan Yang, Donglei Combinatorics We show that for any integer $r\ge 2$, there exists a constant $c>0$ such that for every sufficiently large integer $n$, every $((r-1)n+1)$-regular graph $G$ on $rn$ vertices has at least $c2^{rn}$ subsets $S\subseteq V(G)$ such that $G[S]$ contains a $K_r$-factor. This confirms a conjecture of Draganić, Keevash and Müyesser for large $n$ [Cyclic subsets in regular Dirac graphs. Int. Math. Res. Not., 2025(14): 1-16, 2025]. |
| title | Clique factors in random samplings of regular graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2512.20287 |