4 papers · 1 filter
An Analogue of Quasi-Transitivity for Edge-Coloured Graphs
Christopher Duffy, Todd Mullen
We extend the notion of quasi-transitive orientations of graphs to 2-edge-coloured graphs. By relating quasi-transitive -edge-colourings to an equivalence relation on the edge s…
Complete Graphs and Polyominoes
Todd Mullen, Richard Nowakowski, Danielle Cox
In the chip-firing variant, Diffusion, chips flow from places of high concentration to places of low concentration (or equivalently, from the rich to the poor). We explore this mod…
Counting Path Configurations in Parallel Diffusion
Todd Mullen, Richard Nowakowski, Danielle Cox
Parallel Diffusion is a variant of Chip-Firing introduced in 2018 by Duffy et al. In Parallel Diffusion, chips move from places of high concentration to places of low concentration…
Diffusion: Quiescence and Perturbation
Danielle Cox, Todd Mullen, Richard Nowakowski
Originally proposed by Duffy et al., Diffusion is a variant of chip-firing in which chips from flow from places of high concentration to places of low concentration. In the variant…