7 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…
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…
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…
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…
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…
The ErdÅs-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…