Michael Tait

activity

20132023

most citedThe maximum relaxation time of a random walk

12 citations · 71 across the 46 of their papers we have counts for

collaborators

Showing 2023 · math.COShow all

8 papers · 2 filters

math.CO2023

Forbidden subgraphs and complete partitions

John Byrne, Michael Tait, Craig Timmons

A graph is called an $(r, k)$ -graph if its vertex set can be partitioned into $r$ parts, each having at most $k$ vertices and there is at least one edge between any two parts. Let $…

math.CO2023★ 1 cited

Regular Graphs of Degree at most Four that Allow Two Distinct Eigenvalues

Wayne Barrett, Shaun Fallat, Veronika Furst +3

For an $n \times n$ matrix $A$ , let $q (A)$ be the number of distinct eigenvalues of $A$ . If $G$ is a connected graph on $n$ vertices, let $S (G)$ be the set of all real sy…

math.CO2023

Improved upper bounds on even-cycle creating Hamilton paths

John Byrne, Michael Tait

We study the function $H_{n} (C_{2 k})$ , the maximum number of Hamilton paths such that the union of any pair of them contains $C_{2 k}$ as a subgraph. We give upper bounds on this quan…

math.CO2023★ 1 cited

VC-dimension and pseudo-random graphs

Thang Pham, Steven Senger, Michael Tait +1

Let $G$ be a graph and $U \subset V (G)$ be a set of vertices. For each $v \in U$ , let $h_{v} : U \to {0, 1}$ be the function defined by \[h_v(u)=\begin{cases} &1 ~\mbox{if}~u\sim…

math.CO2023★ 1 cited

Bordering of Symmetric Matrices and an Application to the Minimum Number of Distinct Eigenvalues for the Join of Graphs

Aida Abiad, Shaun M. Fallat, Mark Kempton +5

An important facet of the inverse eigenvalue problem for graphs is to determine the minimum number of distinct eigenvalues of a particular graph. We resolve this question for the j…

math.CO2023

An improved point-line incidence bound over arbitrary finite fields via the VC-dimension theory

Alex Iosevich, Thang Pham, Steven Senger +1

The main purpose of this paper is to prove that the point-line incidence bound due to Vinh (2011) over arbitrary finite fields can be improved in certain ranges by using tools from…

math.CO2023

Extremal values for the spectral radius of the normalized distance Laplacian

Jacob Johnston, Michael Tait

The normalized distance Laplacian of a graph $G$ is defined as $D^{L} (G) = T (G)^{- 1/2} (T (G) - D (G)) T (G)^{- 1/2}$ where $D (G)$ is the matrix with pa…

math.CO2023

Spectral Radii of Arithmetical Structures on Cycle Graphs

Alexander Diaz-Lopez, Kathryn Haymaker, Michael Tait

Let $G$ be a finite, connected graph. An arithmetical structure on $G$ is a pair of positive integer-valued vectors $(d, r)$ such that $(\text{diag}(\mathbf{d})-A_…