William Linz

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20192026

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9 papers · 1 filter

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.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.CO2024

$L$ -systems and the Lovász number

William Linz

Given integers $n > k > 0$ , and a set of integers $L \subset [0, k - 1]$ , an \emph{ $L$ -system} is a family of sets $F \subset (k [ n ])$ such that $∣ F \cap F^{'} ∣ \in L$ …

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…

math.CO2023

Improved lower bounds on the extrema of eigenvalues of graphs

William Linz

In this note, we improve the lower bounds for the maximum size of the $k$ th largest eigenvalue of the adjacency matrix of a graph for several values of $k$ . In particular, we show…

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

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

L-systems and the Lovász number

Some exact and asymptotic results for hypergraph Turán problems in ℓ2​-norm

On the maximum second eigenvalue of outerplanar graphs

Improved lower bounds on the extrema of eigenvalues of graphs

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

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

$L$ -systems and the Lovász number

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