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09/12/2023
The χ-binding function of d-directional segment graphs
Given a positive integer d, the class d-DIR is defined as all those inte...
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08/28/2023
A precise condition for independent transversals in bipartite covers
Given a bipartite graph H=(V=V_A∪ V_B,E) in which any vertex in V_A (res...
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10/11/2021
Packing list-colourings
List colouring is an influential and classic topic in graph theory. We i...
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07/15/2020
An improved procedure for colouring graphs of bounded local density
We develop an improved bound for the chromatic number of graphs of maxim...
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04/15/2020
An algorithmic framework for colouring locally sparse graphs
We develop an algorithmic framework for graph colouring that reduces the...
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12/31/2019
Structure and colour in triangle-free graphs
Motivated by a recent conjecture of the first author, we prove that ever...
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05/15/2019
Strong chromatic index and Hadwiger number
We investigate the effect of a fixed forbidden clique minor upon the str...
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12/28/2018
Occupancy fraction, fractional colouring, and triangle fraction
Given ε>0, there exists f_0 such that, if f_0 < f <Δ^2+1, then for any g...
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12/04/2018
Colouring triangle-free graphs with local list sizes
We prove two distinct and natural refinements of a recent breakthrough r...
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08/07/2018
Bipartite induced density in triangle-free graphs
Any triangle-free graph on n vertices with minimum degree at least d con...
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05/06/2018
Tree-like distance colouring for planar graphs of sufficient girth
Given a multigraph G and a positive integer t, the distance-t chromatic ...
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03/29/2018
Least conflict choosability
Given a multigraph, suppose that each vertex is given a local assignment...
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02/11/2018
