George Brooks

activity

20232026

collaborators

7 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

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.CO2025

Spectral radius and Hamiltonicity of uniform hypergraphs

George Brooks, William Linz, Ruth Luo

Let $n$ and $r$ be integers with $n - 2 \geq r \geq 3$ . We prove that any $r$ -uniform hypergraph $H$ on $n$ vertices with spectral radius $λ (H) > (r - 1 n - 2)$ mu…

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

Outerplanar graphs with positive Lin-Lu-Yau curvature

George Brooks, Fadekemi Osaye, Anna Schenfisch +2

In this paper, we show that all simple outerplanar graphs $G$ with minimum degree at least $2$ and positive Lin-Lu-Yau Ricci curvature on every edge have maximum degree at most $9$ …

math.CO2023

Some exact and asymptotic results for hypergraph Turán problems in $ℓ_{2}$ -norm

George Brooks, William Linz

For a $k$ -uniform hypergraph $H$ , the \emph{codegree squared sum} $co_{2} (H)$ is the square of the $ℓ_{2}$ -norm of the codegree vector of $H$ , a…

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…