3 papers
math.CO2026
A Structural Approach to Burning Number
Jean Guillaume, Tyriana Williams
Graph burning is a deterministic discrete-time process that models the propagation of information within a network as a set of fires that spread in a graph. The associated graph pa…
math.CO2023
Distinguishing chromatic number of Hamiltonian circulant graphs
Michael D. Barrus, Jean Guillaume, Benjamin Lantz
The distinguishing chromatic number of a graph is the smallest number of colors needed to properly color the vertices of so that the trivial automorphism is the only symmet…
math.CO2019
Upward-closed hereditary families in the dominance order
Michael D. Barrus, Jean A. Guillaume
The majorization relation orders the degree sequences of simple graphs into posets called dominance orders. As shown by Ruch and Gutman (1979) and Merris (2002), the degree sequenc…