24 citations · 174 across the 48 of their papers we have counts for
49 papers
Four triangle-free intrinsically knotted graphs with 22 edges
Hyoungjun Kim, Thomas W. Mattman, Seungsang Oh
An intrinsically knotted graph is one for which every spatial embedding contains a nontrivially knotted cycle. Classifying such graphs is a central problem in spatial graph theory.…
Three thousand obstructions to knotless embedding
Thomas W Mattman, Andrei Pavelescu
We present a list of 3028 obstructions to knotless embedding. We survey recent work in this area including: 1) A bibliography of graphs proven to be intrinsically knotted without r…
Galois theory by calculator
Thomas W. Mattman, Dylan Robertson-Figaniak, Zoe Steele
We present an algorithm to determine the Galois group of an irreducible monic polynomial of degree at most five. Following work of Conrad, Dummit, and Stau…
Ihara zeta functions for some simple graph families
Maize Chico, Thomas W. Mattman, Alex Richards
The reciprocal of the Ihara zeta function of a graph is a polynomial invariant introduced by Ihara in 1966. Scott and Storm gave a method to determine the coefficients of the polyn…
COVID on trees and infinite grids
Andrea Barnett, Robert Bond, Anthony Macias +3
We use Hartnell's model for virus spread on a graph, also known as firefighting. For rooted trees, we propose an Unburning Algorithm, a type of greedy algorithm starting from the l…
Non-integral boundary slopes of alternating knots
Masaharu Ishikawa, Thomas W. Mattman, Koya Shimokawa
We show, for every positive integer , there is an alternating knot having a boundary slope with denominator . We make use of Kabaya's method for boundary slopes and the layer…