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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.09027 |
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| _version_ | 1866913697409007616 |
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| author | Ding, Changxin |
| author_facet | Ding, Changxin |
| contents | Csikvári constructed a poset on trees to prove that several graph functions attain extreme values at the star and the path among the trees on a fixed number of vertices. Reiner and Smith proved that the Tutte polynomials $T(1,y)$ of cones over trees, which are the graphs obtained by attaching a cone vertex to a tree, have the described extreme behavior. They further conjectured that the result can be strengthened in terms of Csikvári's poset. We solve this conjecture affirmatively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09027 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Csikvári's poset and Tutte polynomial Ding, Changxin Combinatorics Csikvári constructed a poset on trees to prove that several graph functions attain extreme values at the star and the path among the trees on a fixed number of vertices. Reiner and Smith proved that the Tutte polynomials $T(1,y)$ of cones over trees, which are the graphs obtained by attaching a cone vertex to a tree, have the described extreme behavior. They further conjectured that the result can be strengthened in terms of Csikvári's poset. We solve this conjecture affirmatively. |
| title | Csikvári's poset and Tutte polynomial |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2405.09027 |