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The multiplicative Merino--Welsh inequality for chordal graphs
Abstract
For a connected graph G, let τ(G), α(G) and α*(G) denote its numbers of spanning trees, acyclic orientations and totally cyclic orientations, respectively. We prove that α(G)α*(G)≥τ(G)2 for every connected bridgeless chordal graph.
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BibTeX
@misc{xu2026multiplicative,
title = {{The multiplicative Merino--Welsh inequality for chordal graphs}},
author = {Shaohan Xu and Fengming Dong and Kexiang Xu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25817},
eprint = {2610.25817},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25817},
}
RIS
TY - UNPB
TI - The multiplicative Merino--Welsh inequality for chordal graphs
AU - Shaohan Xu
AU - Fengming Dong
AU - Kexiang Xu
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.25817
UR - https://arxiv.org/abs/2610.25817
AB - For a connected graph G, let τ(G), α(G) and α^*(G) denote its numbers of spanning trees, acyclic orientations and totally cyclic orientations, respectively. We prove that α(G)α^*(G)≥τ(G)^2 for every connected bridgeless chordal graph.
ER -