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04/17/2022
Optimally Reconfiguring List and Correspondence Colourings
The reconfiguration graph 𝒞_k(G) for the k-colourings of a graph G has a...
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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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08/04/2020
Minimum maximal matchings in cubic graphs
We prove that every connected cubic graph with n vertices has a maximal ...
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01/13/2020
Packing and covering balls in graphs excluding a minor
We prove that for every integer t> 1 there exists a constant c_t such th...
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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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12/17/2019
Erdős-Pósa from ball packing
A classic theorem of Erdős and Pósa (1965) states that every graph has e...
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11/28/2019
Large independent sets in triangle-free cubic graphs: beyond planarity
Every n-vertex planar triangle-free graph with maximum degree at most 3 ...
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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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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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07/13/2018