William Linz

activity

20212026

most citedSymmetry and asymmetry between positive and negative square energies of graphs

2 citations · 4 across the 7 of their papers we have counts for

collaborators

8 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.CO2026

Set systems containing no singleton intersection and the Delsarte number

William Linz

We prove that the maximum size of a family of $k$ -element subsets of the set $[n] = {1, 2, \dots, n}$ which contains no singleton intersection is $(k - 2 n - 2)$ when $3k-3 \…

math.CO2025

A remark on the $t$ -intersecting Erdős-Ko-Rado theorem

William Linz

The $t$ -intersecting Erdős-Ko-Rado theorem is the following statement: if $F \subset (k [ n ])$ is a $t$ -intersecting family of sets and $n \geq (t + 1) (k - t + 1)$ , then $|…

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.CO2023★ 2 cited

Symmetry and asymmetry between positive and negative square energies of graphs

Clive Elphick, William Linz

The positive and negative square energies of a graph, $s^{+} (G)$ and $s^{-} (G)$ , are the sums of squares of the positive and negative eigenvalues of the adjacency matrix, respectively.…

math.CO2021★ 2 cited

Two conjectured strengthenings of Turán's theorem

Clive Elphick, William Linz, Pawel Wocjan

We investigate two conjectured spectral graph theoretic strengthenings of Turán's theorem. Let $μ_{1} \geq \dots \geq μ_{n}$ denote the eigenvalues of a graph $G$ with $n$ vertices, $m$ …

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

Generalized Nordhaus--Gaddum Inequalities for Eigenvalues

Set systems containing no singleton intersection and the Delsarte number

A remark on the t-intersecting Erdős-Ko-Rado theorem

Spectral radius and Hamiltonicity of uniform hypergraphs

Maximum spectral gaps of graphs

Symmetry and asymmetry between positive and negative square energies of graphs

Two conjectured strengthenings of Turán's theorem

A remark on the $t$ -intersecting Erdős-Ko-Rado theorem