Tiling randomly perturbed multipartite graphs
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915235717185536 |
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| author | Gomez-Leos, Enrique Martin, Ryan R. |
| author_facet | Gomez-Leos, Enrique Martin, Ryan R. |
| contents | A perfect $K_r$-tiling in a graph $G$ is a collection of vertex-disjoint copies of the graph $K_r$ in $G$ that covers all vertices of $G$. In this paper, we prove that the threshold for the existence of a perfect $K_{r}$-tiling of a randomly perturbed balanced $r$-partite graph on $rn$ vertices is $n^{-2/r}$. This result is a multipartite analog of a theorem of Balogh, Treglown, and Wagner and extends our previous result, which was limited to the bipartite setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07284 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tiling randomly perturbed multipartite graphs Gomez-Leos, Enrique Martin, Ryan R. Combinatorics 05C35, 05C70, 05C80 A perfect $K_r$-tiling in a graph $G$ is a collection of vertex-disjoint copies of the graph $K_r$ in $G$ that covers all vertices of $G$. In this paper, we prove that the threshold for the existence of a perfect $K_{r}$-tiling of a randomly perturbed balanced $r$-partite graph on $rn$ vertices is $n^{-2/r}$. This result is a multipartite analog of a theorem of Balogh, Treglown, and Wagner and extends our previous result, which was limited to the bipartite setting. |
| title | Tiling randomly perturbed multipartite graphs |
| topic | Combinatorics 05C35, 05C70, 05C80 |
| url | https://arxiv.org/abs/2504.07284 |