William Linz

activity

20192026

K_{2, t}

-minor-free graphs

1 citations · 1 across the 11 of their papers we have counts for

collaborators

12 papers

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…

math.CO2022★ 1 cited

Maximum spread of $K_{2, t}$ -minor-free graphs

William Linz, Linyuan Lu, Zhiyu Wang

The spread of a graph $G$ is the difference between the largest and smallest eigenvalues of the adjacency matrix of $G$ . In this paper, we consider the family of graphs which conta…

math.CO2022

On the maximum spread of planar and outerplanar graphs

Zelong Li, William Linz, Linyuan Lu +1

The spread of a graph $G$ is the difference between the largest and smallest eigenvalue of the adjacency matrix of $G$ . Gotshall, O'Brien and Tait conjectured that for sufficiently…

math.CO2022

On the sizes of $t$ -intersecting $k$ -chain-free families

József Balogh, William B. Linz, Balázs Patkós

A set system $F$ is $t$ -\textit{intersecting}, if the size of the intersection of every pair of its elements has size at least $t$ . A set system $F$ is $k$ -\tex…

math.CO2021

$s$ -Catalan numbers and Littlewood-Richardson polynomials

William Linz

In this note, we study two generalizations of the Catalan numbers, namely the $s$ -Catalan numbers and the spin $s$ -Catalan numbers. These numbers first appeared in relation to quan…

math.CO2021

Short proofs of three results about intersecting systems

József Balogh, William Linz

In this note, we give short proofs of three theorems about intersection problems. The first one is a determination of the maximum size of a nontrivial $k$ -uniform, $d$ -wise interse…

math.CO2019

Long rainbow arithmetic progressions

József Balogh, William Linz, Letícia Mattos

Define $T_{k}$ as the minimal $t \in N$ for which there is a rainbow arithmetic progression of length $k$ in every equinumerous $t$ -coloring of $[t n]$ for all $n\in \mathbb{N…

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 K2,t​-minor-free graphs

On the maximum spread of planar and outerplanar graphs

On the sizes of t-intersecting k-chain-free families

s-Catalan numbers and Littlewood-Richardson polynomials

Short proofs of three results about intersecting systems

Long rainbow arithmetic progressions

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

Maximum spread of $K_{2, t}$ -minor-free graphs

On the sizes of $t$ -intersecting $k$ -chain-free families

$s$ -Catalan numbers and Littlewood-Richardson polynomials