collaborators

7 papers

cs.CC2025

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…

math.CO2025

Seeing is not believing in limited visibility cops and robbers

Bojan Bašić, 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…

math.CO2025

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…

math.CO2025

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…

math.CO2025

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

math.CO2024

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…