9 papers
The excluded minors for -gainable and regular biased graphs
Nick Brettell, Rutger Campbell, Daryl Funk +1
We prove that a biased graph is gainable over the group if and only if it contains no minor isomorphic to , , or . We develo…
Blind cop-width and balanced minors of graphs
Hector Buffière, Rutger Campbell, Kevin Hendrey +1
We investigate a pursuit-evasion game on an undirected graph in which a robber, moving at a fixed constant speed, attempts to evade a team of cops who are blind to the robber's loc…
The excluded minors of the class of spike minors
Sam Bastida, Nick Brettell, Rutger Campbell +4
Mayhew et al.\ (2021) posed the problem of showing that the minor-closed class of spikes and their minors has a finite set of excluded minors and describing all of them. In this pa…
Turán's theorem for Dowling geometries
Rutger Campbell, Donggyu Kim, Jorn van der Pol
The Dowling geometry , where is a finite group, is a matroid that generalizes the complete-graphic matroid . We determine the maximum size of an -free su…
Binary matroids and degree-boundedness for pivot-minors
Rutger Campbell, James Davies, Robert Hickingbotham
We prove that for every bipartite graph and positive integer , the class of -subgraph-free graphs excluding as a pivot-minor has bounded average degree. Our pro…
The Erdős-Pósa property for circle graphs as vertex-minors
Rutger Campbell, J. Pascal Gollin, Meike Hatzel +4
We prove that for any circle graph with at least one edge and for any positive integer , there exists an integer so that every graph either has a vertex-minor…
Treewidth, Hadwiger Number, and Induced Minors
Rutger Campbell, James Davies, Marc Distel +7
Treewidth and Hadwiger number are two of the most important parameters in structural graph theory. This paper studies graph classes in which large treewidth implies the existence o…
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…
Optimal bounds for zero-sum cycles. I. Odd order
Rutger Campbell, J. Pascal Gollin, Kevin Hendrey +1
For a finite (not necessarily Abelian) group , let denote the smallest positive integer such that for every labelling of the arcs of the comple…