5 citations · 7 across the 11 of their papers we have counts for
13 papers
Two Relaxations of the Dominating Hadwiger's Conjecture
António Girão, Sergey Norin, Youri Tamitegama +1
Illingworth and Wood recently proposed the Dominating Hadwiger's Conjecture, a strengthening of Hadwiger's Conjecture which asserts that every graph with no dominating -model…
The Dominating 4-Colour Theorem
António Girão, Freddie Illingworth, Bojan Mohar +6
A "dominating -model" in a graph is a sequence of pairwise vertex-disjoint connected subgraphs of , such that whenever every vertex…
A Recolouring Version of a Conjecture of Reed
Lucas De Meyer, Clément Legrand-Duchesne, Jared León +2
Reed conjectured that the chromatic number of any graph is closer to its clique number than to its maximum degree plus one. We consider a recolouring version of this conjecture, wi…
Tight Bounds for Hypercube Minor-Universality
Emma Hogan, Lukas Michel, Alex Scott +3
Benjamini, Kalifa and Tzalik recently proved that there is an absolute constant such that any graph with at most edges and no isolated vertices is a minor of th…
Clustered Colouring of Graph Products
Rutger Campbell, J. Pascal Gollin, Kevin Hendrey +5
A colouring of a graph has clustering if the maximum number of vertices in a monochromatic component equals . Motivated by recent results showing that many natural graph…
Small families of partially shattering permutations
António Girão, Lukas Michel, Youri Tamitegama
We say that a family of permutations -shatters a set if it induces at least distinct permutations on that set. What is the minimum number of permutations of $\{1,…
A note on graphs of -colourings
Emma Hogan, Alex Scott, Youri Tamitegama +1
For a graph , the -colouring graph of has vertices corresponding to proper -colourings of and edges between colourings that differ at a single vertex. The graph su…
Reconstruction of shredded random matrices
Paul Balister, Gal Kronenberg, Alex Scott +1
A matrix is given in ``shredded'' form if we are presented with the multiset of rows and the multiset of columns, but not told which row is which or which column is which. The matr…
Boundary rigidity of 3D CAT(0) cube complexes
John Haslegrave, Alex Scott, Youri Tamitegama +1
The boundary rigidity problem is a classical question from Riemannian geometry: if is a Riemannian manifold with smooth boundary, is the geometry of determined up to i…
A note on interval colourings of graphs
Maria Axenovich, António Girão, Lawrence Hollom +5
A graph is said to be interval colourable if it admits a proper edge-colouring using palette in which the set of colours incident to each vertex is an interval. The in…
Product structure of graph classes with bounded treewidth
Rutger Campbell, Katie Clinch, Marc Distel +8
We show that many graphs with bounded treewidth can be described as subgraphs of the strong product of a graph with smaller treewidth and a bounded-size complete graph. To this end…
Balancing connected colourings of graphs
Freddie Illingworth, Emil Powierski, Alex Scott +1
We show that the edges of any graph containing two edge-disjoint spanning trees can be blue/red coloured so that the blue and red graphs are connected and the blue and red degr…
Induced subgraphs of induced subgraphs of large chromatic number
António Girão, Freddie Illingworth, Emil Powierski +4
We prove that, for every graph with at least one edge, there is a constant such that there are graphs of arbitrarily large chromatic number and the same clique number as…