16 citations · 20 across the 11 of their papers we have counts for
13 papers · 1 filter
Strong edge-colouring via local flag algebras
Eoin Davey, Eoin Hurley, Rémi de Joannis de Verclos +2
The strong chromatic index is the smallest number of colours needed to colour the edges of a graph so that any two edges at distance at most receive different col…
Local flag algebras
Eoin Davey, Eoin Hurley, Rémi de Joannis de Verclos +2
We introduce local flag algebras, a variant of Razborov's flag algebra framework in which densities are normalised by the maximum degree rather than the order . The fra…
Cycle-factors of regular graphs via entropy
Micha Christoph, Nemanja Draganić, António Girão +3
It is a classical result that a random permutation of elements has, on average, about cycles. We generalise this fact to all directed -regular graphs on vertice…
New bounds for linear arboricity and related problems
Micha Christoph, Nemanja Draganić, António Girão +3
A linear forest is a collection of vertex-disjoint paths. The Linear Arboricity Conjecture states that every graph of maximum degree can be decomposed into at most $\lceil(Δ+1)…
Asymmetric results about graph homomorphisms
Lior Gishboliner, Eoin Hurley, Yuval Wigderson
Many important results in extremal graph theory can be roughly summarised as "if a triangle-free graph has certain properties, then it has a homomorphism to a triangle-free gra…
Upper bounds for multicolour Ramsey numbers
Paul Balister, Béla Bollobás, Marcelo Campos +5
The -colour Ramsey number is the minimum such that every -colouring of the edges of the complete graph on vertices contains a monochroma…
Embedding induced trees in sparse expanding graphs
António Girão, Eoin Hurley
Inspired by the network routing literature \cite{aggarwal1996efficient}, we develop what we call a ``Pre-Emptive Greedy Algorithm" to embed bounded degree induced trees in sparse e…
Abundance: Asymmetric Graph Removal Lemmas and Integer Solutions to Linear Equations
António Girão, Eoin Hurley, Freddie Illingworth +1
We prove that a large family of pairs of graphs satisfy a polynomial dependence in asymmetric graph removal lemmas. In particular, we give an unexpected answer to a question of Gis…
Uniformly Random Colourings of Sparse Graphs
Eoin Hurley, François Pirot
We analyse uniformly random proper -colourings of sparse graphs with maximum degree in the regime . This regime corresponds to the lower side of the shattering t…
Tower Gaps in Multicolour Ramsey Numbers
Quentin Dubroff, António Girão, Eoin Hurley +1
Resolving a problem of Conlon, Fox, and Rödl, we construct a family of hypergraphs with arbitrarily large tower height separation between their -colour and -colour Ramsey num…
Sufficient conditions for perfect mixed tilings
Eoin Hurley, Felix Joos, Richard Lang
We develop a method to study sufficient conditions for perfect mixed tilings. Our framework allows the embedding of bounded degree graphs with components of sublinear order. As…
Colouring locally sparse graphs with the first moment method
François Pirot, Eoin Hurley
We give a short proof of a bound on the list chromatic number of graphs of maximum degree where each neighbourhood has density at most , namely $χ_\ell(G) \le (1+o(1)) \…
An improved procedure for colouring graphs of bounded local density
Eoin Hurley, Rémi de Joannis de Verclos, Ross J. Kang
We develop an improved bound for the chromatic number of graphs of maximum degree under the assumption that the number of edges spanning any neighbourhood is at most $(1-σ)\bin…