12 citations · 71 across the 46 of their papers we have counts for
8 papers · 1 filter
Forbidden subgraphs and complete partitions
John Byrne, Michael Tait, Craig Timmons
A graph is called an -graph if its vertex set can be partitioned into parts, each having at most vertices and there is at least one edge between any two parts. Let $…
Regular Graphs of Degree at most Four that Allow Two Distinct Eigenvalues
Wayne Barrett, Shaun Fallat, Veronika Furst +3
For an matrix , let be the number of distinct eigenvalues of . If is a connected graph on vertices, let be the set of all real sy…
Improved upper bounds on even-cycle creating Hamilton paths
John Byrne, Michael Tait
We study the function , the maximum number of Hamilton paths such that the union of any pair of them contains as a subgraph. We give upper bounds on this quan…
VC-dimension and pseudo-random graphs
Thang Pham, Steven Senger, Michael Tait +1
Let be a graph and be a set of vertices. For each , let be the function defined by \[h_v(u)=\begin{cases} &1 ~\mbox{if}~u\sim…
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…
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…