41 citations · 175 across the 19 of their papers we have counts for
15 papers · 1 filter
List packing number of bounded degree graphs
Stijn Cambie, Wouter Cames van Batenburg, Ewan Davies +1
We investigate the list packing number of a graph, the least such that there are always disjoint proper list-colourings whenever we have lists all of size associated to…
Packing list-colourings
Stijn Cambie, Wouter Cames van Batenburg, Ewan Davies +1
List colouring is an influential and classic topic in graph theory. We initiate the study of a natural strengthening of this problem, where instead of one list-colouring, we seek m…
The -Ramsey problem for triangle-free graphs
Ewan Davies, Freddie Illingworth
In 1967, Erdős asked for the greatest chromatic number, , amongst all -vertex, triangle-free graphs. An observation of Erdős and Hajnal together with Shearer's classical u…
A proof of the Upper Matching Conjecture for large graphs
Ewan Davies, Matthew Jenssen, Will Perkins
We prove that the `Upper Matching Conjecture' of Friedland, Krop, and Markström and the analogous conjecture of Kahn for independent sets in regular graphs hold for all large enoug…
Graph structure via local occupancy
Ewan Davies, Ross J. Kang, François Pirot +1
The first author together with Jenssen, Perkins and Roberts (2017) recently showed how local properties of the hard-core model on triangle-free graphs guarantee the existence of la…
Regularity inheritance in hypergraphs
Peter Allen, Ewan Davies, Jozef Skokan
We give a new approach to handling hypergraph regularity. This approach allows for vertex-by-vertex embedding into regular partitions of hypergraphs, and generalises to regular par…
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…
Tight bounds on the coefficients of partition functions via stability
Ewan Davies, Matthew Jenssen, Will Perkins +1
Partition functions arise in statistical physics and probability theory as the normalizing constant of Gibbs measures and in combinatorics and graph theory as graph polynomials. Fo…
Extremes of the internal energy of the Potts model on cubic graphs
Ewan Davies, Matthew Jenssen, Will Perkins +1
We prove tight upper and lower bounds on the internal energy per particle (expected number of monochromatic edges per vertex) in the anti-ferromagnetic Potts model on cubic graphs…
On the average size of independent sets in triangle-free graphs
Ewan Davies, Matthew Jenssen, Will Perkins +1
We prove an asymptotically tight lower bound on the average size of independent sets in a triangle-free graph on vertices with maximum degree , showing that an independent s…
Multicolour Ramsey numbers of paths and even cycles
Ewan Davies, Matthew Jenssen, Barnaby Roberts
We prove new upper bounds on the multicolour Ramsey numbers of paths and even cycles. It is well known that . The upper bound was…
Independent Sets, Matchings, and Occupancy Fractions
Ewan Davies, Matthew Jenssen, Will Perkins +1
We prove tight upper bounds on the logarithmic derivative of the independence and matching polynomials of d-regular graphs. For independent sets, this theorem is a strengthening of…