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math.CO2020
On lengths of burn-off chip-firing games
P. Mark Kayll, Dave Perkins
We continue our studies of burn-off chip-firing games from [Discrete Math. Theor. Comput. Sci. 15 (2013), no. 1, 121-132; MR3040546] and [Australas. J. Combin. 68 (2017), no. 3, 33…
math.CO2020
Uniquely -colourable digraphs with large girth II: simplification via generalization
P. Mark Kayll, Esmaeil Parsa
We prove that for every digraph and every choice of positive integers , there exists a digraph with girth at least together with a surjective acyclic hom…