George Brooks

activity

20242026

collaborators

6 papers

math.CO2026

Generalized Nordhaus--Gaddum Inequalities for Eigenvalues

Sahil Agarwal, Carter Antley, Joseph Aulenbacher +6

For a graph $G$ , let $I^»_{1} (G) \geq I^»_{2} (G) \geq \dots \geq I^»_{n} (G)$ denote the adjacency eigenvalues of $G$ . We investigate the asymptotic maximum of \[ Î»_i(G)+Î»_j(\overline G) \] f…

math.CO2026

Some exact and asymptotic results for hypergraph TurÃ¡n 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.CO2026

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 $I^» (H) > (r - 1 n - 2)$ m…

math.CO2025

Maximum spectral gaps of graphs

George Brooks, William Linz, Linyuan Lu

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

math.CO2025

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.CO2024

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 $I^»_{k} (G)$ denote the $k$ -th largest eigenvalue of the adjacency matrix of $G$ . In 2017, Tait and Tobin proved that the maximum…

Generalized Nordhaus--Gaddum Inequalities for Eigenvalues

Some exact and asymptotic results for hypergraph TurÃ¡n problems in ℓ2​-norm

Spectral radius and Hamiltonicity of uniform hypergraphs

Maximum spectral gaps of graphs

Outerplanar graphs with positive Lin-Lu-Yau curvature

On the maximum second eigenvalue of outerplanar graphs

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