9 citations · 9 across the 7 of their papers we have counts for
7 papers · 1 filter
On colouring oriented graphs of large girth
P. Mark Kayll, Michael Morris
We prove that for every oriented graph and every choice of positive integers and , there exists an oriented graph along with a surjective homomorphism $ψ\colon…
Deranged matchings: proofs and conjectures
Daniel Johnston, P. Mark Kayll, Cory Palmer
We introduce, and partially resolve, a conjecture that brings a three-centuries-old derangements phenomenon and its much younger two-decades-old analogue under the same umbrella. T…
Egerváry graphs: Deming decompositions and independence structure
P. Mark Kayll, Craig E. Larson
We leverage an algorithm of Deming [R.W. Deming, Independence numbers of graphs -- an extension of the Koenig-Egervary theorem, Discrete Math., 27(1979), no. 1, 23--33; MR534950] t…
On random digraphs and cores
Esmaeil Parsa, P. Mark Kayll
An acyclic homomorphism of a digraph to a digraph is a function such that for every arc of , either , or is an arc of $…
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…
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…
Uniquely D-colourable digraphs with large girth
Ararat Harutyunyan, P. Mark Kayll, Bojan Mohar +1
Let C and D be digraphs. A mapping is a C-colouring if for every arc of D, either is an arc of C or , and the preimage of every vertex o…