Michael Tait

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20242026

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4 papers · 1 filter

math.CO2024

Graphs with Bipartite Complement that Admit Two Distinct Eigenvalues

Wayne Barrett, Shaun Fallat, Veronika Furst +3

The parameter $q (G)$ of an $n$ -vertex graph $G$ is the minimum number of distinct eigenvalues over the family of symmetric matrices described by $G$ . We show that all $G$ with $e(\…

math.CO2024

Turán numbers for non-bipartite graphs and applications to spectral extremal problems

Longfei Fang, Michael Tait, Mingqing Zhai

Given a graph family $H$ with $min_{H \in H} χ (H) = r + 1 \geq 3$ . Let $ex (n, H)$ and $spex (n, H)$ be the maximum number of edges and th…

math.CO2024

Hypergraphs of girth 5 and 6 and coding theory

Kathryn Haymaker, Michael Tait, Craig Timmons

In this paper, we study the maximum number of edges in an $N$ -vertex $r$ -uniform hypergraph with girth $g$ where $g \in {5, 6}$ . Writing $ex_{r} (N, C_{< g})$ f…

math.CO2024

A general theorem in spectral extremal graph theory

John Byrne, Dheer Noal Desai, Michael Tait

The extremal graphs $EX (n, F)$ and spectral extremal graphs $SPEX (n, F)$ are the sets of graphs on $n$ vertices with maximum number of edges and m…