7 papers
Misère Partizan Arc Kayles is PSPACE-complete, even on Planar Graphs
Kyle Burke, Caroline Cashman, Alfie Davies +2
We show that Misère Partizan Arc Kayles is PSPACE-complete on planar graphs via a reduction from Bounded Two-Player Constraint Logic. Furthermore, we show how to embed our gadgets…
Seeing is not believing in limited visibility cops and robbers
Bojan BaÅ¡iÄ, Alfie Davies, Aleksa Džuklevski +2
We consider the model of limited visibility Cops and Robbers, where the cops can only see within their -neighbourhood. We prove that the number of cops needed to see the robber…
On graph automorphisms related to Snort
Rylo Ashmore, Beth Ann Austin, Alfie M. Davies +2
We study the outcomes of various positions of the game Snort. When played on graphs admitting an automorphism of order two that maps vertices outside of their closed neighbourhoods…
On sums of -free forms under misère play
Alfie Davies, Sarah Miller, Rebecca Milley
Milley and Renault proved an interesting characterisation of invertible elements in the dead-ending universe: they are the games with no subpositions of outcome (the…
Constructing All Birthday 3 Games as Digraphs
Alexander Clow, Alfie Davies, Neil Anderson McKay
Recently, Clow and McKay proved that the Digraph Placement ruleset is universal for normal play: for all normal play combinatorial games , there is a Digraph Placement game …
Invertibility in the misère multiverse
Alfie Davies, Vishal Yadav
Understanding invertibility in restricted misère play has been challenging; in particular, the possibility of non-conjugate inverses posed difficulties. Advances have been made in…