Linyuan Lu

activity

20192026

most citedOn Hamiltonian Berge cycles in

3

-uniform hypergraphs

3 citations · 3 across the 12 of their papers we have counts for

collaborators

12 papers

math.CO2026

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 $d$ -regular graphs with positive Lin--Lu--Yau (LLY) curvature. We show that any positively curved $d$ -regular graph…

math.CO2026

Maximum spread of $K_{s, t}$ -minor-free graphs II: the non-admissible cases

William Linz, Linyuan Lu, Zhiyu Wang

We have previously determined the maximum-spread $K_{s, t}$ -minor-free graph(s) on $n$ vertices when $n$ is sufficiently large, $2 \leq s \leq t$ , and $s = 2$ or $t\ge \frac{3}{2}(s-3) +…

math.CO2026

Generalized Nordhaus--Gaddum Inequalities for Eigenvalues

Sahil Agarwal, Carter Antley, Joseph Aulenbacher +6

For a graph $G$ , let $λ_{1} (G) \geq λ_{2} (G) \geq \dots \geq λ_{n} (G)$ denote the adjacency eigenvalues of $G$ . We prove that for all looped graphs $G$ on $n$ vertices, \[λ_1(G) + λ_2(\over…

math.CO2026

Turán-Type Bounds for Graphs Containing Large $F$ -Sparse Sets

Yupei Li, Linyuan Lu

We study Turán-type extremal problems for graphs containing a large $F$ -sparse vertex set, meaning a vertex set whose induced subgraph contains few copies of $F$ . For integers $r>s…

math.CO2025

An Ore-type theorem for $[3]$ -graphs

Yupei Li, Linyuan Lu, Ruth Luo

Ore's Theorem states that if $G$ is an $n$ -vertex graph and every pair of non-adjacent vertices has degree sum at least $n$ , then $G$ is Hamiltonian. A $[3]$ -graph is a hypergraph…

math.CO2024

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 $G$ with minimum degree at least $2$ has positive Lin-Lu-Yau curvature o…

math.CO2024

Ricci Curvature Formula: Applications to Bonnet-Myers Sharp Irregular Graphs

Yupei Li, Linyuan Lu

In this paper, we establish a simple formula for computing the Lin-Lu-Yau Ricci curvature on graphs. For any edge $x y$ in a simple locally finite graph $G$ , the curvature $κ (x, y)$ …

math.CO2024

Maximum spectral gaps of graphs

George Brooks, William Linz, Linyuan Lu

The spread of a graph $G$ is the difference $λ_{1} - λ_{n}$ between the largest and smallest eigenvalues of its adjacency matrix. Breen, Riasanovsky, Tait and Urschel recently determin…

math.CO2024

Maximum spread of $K_{s, t}$ -minor-free graphs

William Linz, Linyuan Lu, Zhiyu Wang

The spread of a graph $G$ is the difference between the largest and smallest eigenvalue of the adjacency matrix of $G$ . In this paper, we consider the family of graphs which contai…

math.CO2023

A tight bound on ${C_{3}, C_{5}}$ -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 ${C_{3}, C_{5}}$ -free non-empty connected graph $G$ with LLY curvature bounded below by $κ > 0$ has the order at most $2^{\frac{2}{κ}}$ . This upper…

math.CO2023

On the maximum second eigenvalue of outerplanar graphs

George Brooks, Maggie Gu, Jack Hyatt +2

For a fixed positive integer $k$ and a graph $G$ , let $λ_{k} (G)$ denote the $k$ -th largest eigenvalue of the adjacency matrix of $G$ . In 2017, Tait and Tobin proved that the maximum…

math.CO2019★ 3 cited

On Hamiltonian Berge cycles in $3$ -uniform hypergraphs

Linyuan Lu, Zhiyu Wang

Given a set $R$ , a hypergraph is $R$ -uniform if the size of every hyperedge belongs to $R$ . A hypergraph $H$ is called \textit{covering} if every vertex pair is contained…

On the classification of regular graphs with positive Lin-Lu-Yau curvature

Maximum spread of Ks,t​-minor-free graphs II: the non-admissible cases

Generalized Nordhaus--Gaddum Inequalities for Eigenvalues

Turán-Type Bounds for Graphs Containing Large F-Sparse Sets

An Ore-type theorem for [3]-graphs

On the size of outerplanar graphs with positive Lin-Lu-Yau Ricci curvature

Ricci Curvature Formula: Applications to Bonnet-Myers Sharp Irregular Graphs

Maximum spectral gaps of graphs

Maximum spread of Ks,t​-minor-free graphs

A tight bound on {C3​,C5​}-free connected graphs with positive Lin-Lu-Yau Ricci curvature

On the maximum second eigenvalue of outerplanar graphs

On Hamiltonian Berge cycles in 3-uniform hypergraphs

Maximum spread of $K_{s, t}$ -minor-free graphs II: the non-admissible cases

Turán-Type Bounds for Graphs Containing Large $F$ -Sparse Sets

An Ore-type theorem for $[3]$ -graphs

Maximum spread of $K_{s, t}$ -minor-free graphs

A tight bound on ${C_{3}, C_{5}}$ -free connected graphs with positive Lin-Lu-Yau Ricci curvature

On Hamiltonian Berge cycles in $3$ -uniform hypergraphs