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On the maximum degree and order of Kt-minor-free graphs with positive Lin--Lu--Yau curvature
Abstract
Motivated by recent results on the order of connected graphs with positive Lin--Lu--Yau Ricci curvature under forbidden minor or forbidden subgraph conditions and minimum degree assumptions, we prove that, for every integer t≥ 5, every locally finite graph G with no Kt minor, minimum degree at least t−1 and positive Lin--Lu--Yau Ricci curvature on every edge satisfies Δ(G)=O(t5log3/2t). The minimum degree condition t−1 is best possible. Moreover, if G is connected, then G is finite and |V(G)|<2tΔ(G)6=O(t31log9 t).
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BibTeX
@misc{song2026maximum,
title = {{On the maximum degree and order of $K_t$-minor-free graphs with positive Lin--Lu--Yau curvature}},
author = {Zi-Xia Song},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08706},
eprint = {2610.08706},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08706},
}
RIS
TY - UNPB
TI - On the maximum degree and order of K_t-minor-free graphs with positive Lin--Lu--Yau curvature
AU - Zi-Xia Song
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.08706
UR - https://arxiv.org/abs/2610.08706
AB - Motivated by recent results on the order of connected graphs with positive Lin--Lu--Yau Ricci curvature under forbidden minor or forbidden subgraph conditions and minimum degree assumptions, we prove that, for every integer t≥ 5, every locally finite graph G with no K_t minor, minimum degree at least t−1 and positive Lin--Lu--Yau Ricci curvature on every edge satisfies Δ(G)=O(t^5log^3/2t). The minimum degree condition t−1 is best possible. Moreover, if G is connected, then G is finite and |V(G)|<2tΔ(G)^6=O(t^31log^9 t).
ER -