An Ore-type condition for $H$-tilings in graphs
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913153851326464 |
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| author | Gao, Yuping Guo, Yilin Wang, Guanghui Zhang, Lin-Peng |
| author_facet | Gao, Yuping Guo, Yilin Wang, Guanghui Zhang, Lin-Peng |
| contents | A graph $G$ admits an $H$-tiling if it contains a collection of vertex-disjoint copies of $H$. In this paper, we confirm a conjecture proposed by Kühn, Osthus, and Treglown by showing that for any given graph $H$, there exists a constant $C(H)$ such that the following holds. If $G$ is a sufficiently large $n$-vertex graph satisfying $d(x) + d(y) \geq 2\left(1 - 1/χ_{\text{cr}}(H)\right)n$ for all nonadjacent vertices $x, y \in V(G)$, then $G$ contains an $H$-tiling covering all but at most $C(H)$ vertices. Here $χ_{\text{cr}}(H)$ denotes the critical chromatic number of $H$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_22553 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An Ore-type condition for $H$-tilings in graphs Gao, Yuping Guo, Yilin Wang, Guanghui Zhang, Lin-Peng Combinatorics A graph $G$ admits an $H$-tiling if it contains a collection of vertex-disjoint copies of $H$. In this paper, we confirm a conjecture proposed by Kühn, Osthus, and Treglown by showing that for any given graph $H$, there exists a constant $C(H)$ such that the following holds. If $G$ is a sufficiently large $n$-vertex graph satisfying $d(x) + d(y) \geq 2\left(1 - 1/χ_{\text{cr}}(H)\right)n$ for all nonadjacent vertices $x, y \in V(G)$, then $G$ contains an $H$-tiling covering all but at most $C(H)$ vertices. Here $χ_{\text{cr}}(H)$ denotes the critical chromatic number of $H$. |
| title | An Ore-type condition for $H$-tilings in graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2605.22553 |