3 papers
math.CO2026
Chains and unique transitive orientations of prime graphs
Robert Brignall, Sean Mandrick, Vincent Vatter
We give a short, conceptual proof that prime graphs have at most two transitive orientations, a much-quoted result of Gallai. Our proof uses chains, introduced by Chudnovsky, Kim,…
math.CO2025
On Inversion Graphs of Permutations
Sean Mandrick
In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where verti…
math.CO2023
Bounds on the lettericity of graphs
Sean Mandrick, Vincent Vatter
Lettericity measures the minimum size of an alphabet needed to represent a graph as a letter graph, where vertices are encoded by letters, and edges are determined by an underlying…