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Positively Lin-Lu-Yau curved graphs with no K2,t minor
Abstract
Let G be a connected graph with minimum degree at least two, positive Lin-Lu-Yau Ricci curvature, and no K2,t minor, where t≥ 3 is an integer. We first establish tight upper bounds on the maximum degree of G by showing that Δ(G)≤ 2t+3 for t=4, Δ(G)≤ 2t+4 for t∈{5,6}, and Δ(G)≤ 2t+2 for all t≥7. We then prove that G has at most $10$ vertices for t=3, and at most (t+1)(Δ(G)2(Δ(G)−1)/2+1) vertices for all t≥ 4.
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BibTeX
@misc{bai2026positively,
title = {{Positively Lin-Lu-Yau curved graphs with no $K_2,t$ minor}},
author = {Shuliang Bai and Xiaonan Liu and Zi-Xia Song},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05519},
eprint = {2610.05519},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05519},
}
RIS
TY - UNPB
TI - Positively Lin-Lu-Yau curved graphs with no K_2,t minor
AU - Shuliang Bai
AU - Xiaonan Liu
AU - Zi-Xia Song
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05519
UR - https://arxiv.org/abs/2610.05519
AB - Let G be a connected graph with minimum degree at least two, positive Lin-Lu-Yau Ricci curvature, and no K_2,t minor, where t≥ 3 is an integer. We first establish tight upper bounds on the maximum degree of G by showing that Δ(G)≤ 2t+3 for t=4, Δ(G)≤ 2t+4 for t∈{5,6}, and Δ(G)≤ 2t+2 for all t≥7. We then prove that G has at most $10$ vertices for t=3, and at most (t+1)(Δ(G)^2(Δ(G)−1)/2+1) vertices for all t≥ 4.
ER -