William Linz

collaborators

5 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

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.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

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

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

William Linz

The $t$ -intersecting ErdÅs-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 $…

Generalized Nordhaus--Gaddum Inequalities for Eigenvalues

Spectral radius and Hamiltonicity of uniform hypergraphs

Set systems containing no singleton intersection and the Delsarte number

Maximum spectral gaps of graphs

A remark on the t-intersecting ErdÅs-Ko-Rado theorem

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