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arXiv · 2405.09027

Csikvári's poset and Tutte polynomial

Changxin Ding
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Abstract

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.

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Changxin Ding. 2025-02-19. Csikvári's poset and Tutte polynomial. https://arxiv.org/abs/2405.09027

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