6 citations · 34 across the 27 of their papers we have counts for
6 papers · 1 filter
Treewidth, Circle Graphs and Circular Drawings
Robert Hickingbotham, Freddie Illingworth, Bojan Mohar +1
A circle graph is an intersection graph of a set of chords of a circle. We describe the unavoidable induced subgraphs of circle graphs with large treewidth. This includes examples…
Notes on Aharoni's rainbow cycle conjecture
Katie Clinch, Jackson Goerner, Tony Huynh +1
In 2017, Ron Aharoni made the following conjecture about rainbow cycles in edge-coloured graphs: If is an -vertex graph whose edges are coloured with colours and each co…
Defective Colouring of Hypergraphs
António Girão, Freddie Illingworth, Alex Scott +1
We prove that the vertices of every -uniform hypergraph with maximum degree may be coloured with colours such that each vertex is in at most $…
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…