37 citations · 312 across the 39 of their papers we have counts for
7 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…
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.…
Bipartite induced density in triangle-free graphs
Wouter Cames van Batenburg, Rémi de Joannis de Verclos, Ross J. Kang +1
We prove that any triangle-free graph on vertices with minimum degree at least contains a bipartite induced subgraph of minimum degree at least . This is sharp up…
VC dimension and a union theorem for set systems
Stijn Cambie, António Girão, Ross J. Kang
Fix positive integers and . We show that, as , any set system for which the VC dimension of $\{ \triangle_{i=1}^k S_i \mid S_i \in…
Tree-like distance colouring for planar graphs of sufficient girth
Ross J. Kang, Willem van Loon
Given a multigraph and a positive integer , the distance- chromatic index of is the least number of colours needed for a colouring of the edges so that every pair of…
Single-conflict colouring
Zdeněk Dvořák, Louis Esperet, Ross J. Kang +1
Given a multigraph, suppose that each vertex is given a local assignment of colours to its incident edges. We are interested in whether there is a choice of one local colour pe…
Separation choosability and dense bipartite induced subgraphs
Louis Esperet, Ross J. Kang, Stéphan Thomassé
We study a restricted form of list colouring, for which every pair of lists that correspond to adjacent vertices may not share more than one colour. The optimal list size such that…