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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.11450 |
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| _version_ | 1866913658619035648 |
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| author | Chen, Nannan Liu, Xizhi Sun, Lin Wang, Guanghui |
| author_facet | Chen, Nannan Liu, Xizhi Sun, Lin Wang, Guanghui |
| contents | We determine asymptotically the two extremal constructions for the tiling problem of the $H$-shaped tree. In particular, the first extremal construction is close to the complement of two cliques, in contrast to previously studied bipartite graphs, where the first extremal construction is close to the complement of a single clique. This result refutes one of Lang's conjectures [arXiv:2308.12281], which seeks to generalize the Erdős Matching Conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11450 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tiling $H$ in dense graphs Chen, Nannan Liu, Xizhi Sun, Lin Wang, Guanghui Combinatorics We determine asymptotically the two extremal constructions for the tiling problem of the $H$-shaped tree. In particular, the first extremal construction is close to the complement of two cliques, in contrast to previously studied bipartite graphs, where the first extremal construction is close to the complement of a single clique. This result refutes one of Lang's conjectures [arXiv:2308.12281], which seeks to generalize the Erdős Matching Conjecture. |
| title | Tiling $H$ in dense graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2501.11450 |