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arXiv · 2605.03470

Criteria on forbidden subgraphs in the complements for positive Lin--Lu--Yau curvature

Kaizhe Chen·Shiping Liu·Zhe You
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Abstract

We investigate forbidden subgraph conditions in the complement of a graph that guarantee positive Lin--Lu--Yau curvature. In particular, we prove that every graph whose complement contains no $4$-cycles has positive Lin--Lu--Yau curvature, with the only exception of the $4$-vertex path. We further prove that, for any integer $t\ge2$, every graph on at least $\max\{t^2-2t+2, 8t\}$ vertices whose complement contains no $K_{2,t}$ has positive curvature. In addition, this lower bound on the number of vertices is optimal for $t\geq 10$. Finally, we construct examples showing that, in general, the forbidden subgraphs in these results cannot be replaced by cycles of length other than $4$ or by complete bipartite graphs $K_{s,t}$ with $s> 2$ and $t> 2$.

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Kaizhe Chen, Shiping Liu, Zhe You. 2026-05-05. Criteria on forbidden subgraphs in the complements for positive Lin--Lu--Yau curvature. https://arxiv.org/abs/2605.03470

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