41 citations · 175 across the 19 of their papers we have counts for
4 papers · 1 filter
Occupancy fraction, fractional colouring, and triangle fraction
Ewan Davies, Rémi de Joannis de Verclos, Ross J. Kang +1
Given , there exists such that, if , then for any graph on vertices of maximum degree in which the neighbourhood of every vert…
On zero-free regions for the anti-ferromagnetic Potts model on bounded-degree graphs
Ferenc Bencs, Ewan Davies, Viresh Patel +1
For a graph , , and a complex number the partition function of the univariate Potts model is defined as \[ {\bf Z}(G;k,w):=\sum_{ϕ:V\to [k]}\prod_{\su…
Colouring triangle-free graphs with local list sizes
Ewan Davies, Rémi de Joannis de Verclos, Ross J. Kang +1
We prove two distinct and natural refinements of a recent breakthrough result of Molloy (and a follow-up work of Bernshteyn) on the (list) chromatic number of triangle-free graphs.…
Counting proper colourings in 4-regular graphs via the Potts model
Ewan Davies
We give tight upper and lower bounds on the internal energy per particle in the antiferromagnetic -state Potts model on -regular graphs, for . This proves the first c…