6 papers
On the classification of regular graphs with positive Lin-Lu-Yau curvature
George Brooks, Nathanael Johnson, William Linz +3
We prove several new structural and classification results about -regular graphs with positive Lin--Lu--Yau (LLY) curvature. We show that any positively curved -regular graph…
Counting -cycles in -connected planar triangulations
Gyaneshwar Agrahari, Xiaonan Liu, Zhiyu Wang
We show that every -vertex -connected planar triangulation has at most many cycles of length for all and this upper bound is tight. We also show that fo…
On the size of outerplanar graphs with positive Lin-Lu-Yau Ricci curvature
Xiaonan Liu, Linyuan Lu, Zhiyu Wang
In this paper, extending a result of Brooks et.al. [arXiv:2403.04110], we show that if an outerplanar graph with minimum degree at least has positive Lin-Lu-Yau curvature o…
On tight -stable graphs
Xiaonan Liu, Zi-Xia Song, Zhiyu Wang
For integers , a graph is -stable if for every with . A recent result of Dong and Wu [SIAM J. Discrete Mat…
A tight bound on -free connected graphs with positive Lin-Lu-Yau Ricci curvature
E. G. K. M. Gamlath, Xiaonan Liu, Linyuan Lu +1
In this paper, we prove that any simple -free non-empty connected graph with LLY curvature bounded below by has the order at most . This upper…
On the oriented diameter of near planar triangulations
Yiwei Ge, Xiaonan Liu, Zhiyu Wang
In this paper, we show that the oriented diameter of any -vertex -connected near triangulation is at most (except for seven small exceptions), and…