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math.CO2025

On the hat guessing number of a planar graph class

Peter Bradshaw

The hat guessing number is a graph invariant based on a hat guessing game introduced by Winkler. Using a new vertex decomposition argument involving an edge density theorem of ErdÅ…

math.CO2025

Single-conflict colorings of degenerate graphs

Peter Bradshaw, Tomáš Masařík

We consider the single-conflict coloring problem, a graph coloring problem in which each edge of a graph receives a forbidden ordered color pair. The task is to find a vertex color…

math.CO2024

Hamiltonicity of covering graphs of trees

Peter Bradshaw, Zhilin Ge, Ladislav Stacho

In this paper, we consider covering graphs obtained by lifting a tree with a loop at each vertex as a voltage graph over a cyclic group. We generalize a tool of Hell, Nishiyama, an…

math.CO2024

List-avoiding orientations

Peter Bradshaw, Yaobin Chen, Hao Ma +2

Given a graph with a set of forbidden values at each , an -avoiding orientation of is an orientation in which for each vertex…