10 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…
A Brooks-type theorem for the k-choosability of graphs with maximum local edge-connectivity k
Sam Bastida, Nick Brettell
For a graph with at least two vertices, the maximum local edge-connectivity of is the maximum number of edge-disjoint -paths over all distinct pairs of vertices $(u,…
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…
Non-crossing -graphs: a generalization of proper interval graphs admitting FPT algorithms
Flavia Bonomo-Braberman, Nick Brettell, Noleen Köhler +2
We prove new parameterized complexity results for the FO Model Checking problem on a well-known generalization of interval and circular-arc graphs: the class of -graphs, for any…
Detachable pairs in -connected matroids and simple -connected graphs
Nick Brettell, Charles Semple, Gerry Toft
Let be a -connected matroid. A pair in is detachable if or is -connected. Williams (2015) proved that if has a…
Comparing Width Parameters on Graph Classes
Nick Brettell, Andrea Munaro, Daniël Paulusma +1
We study how the relationship between non-equivalent width parameters changes once we restrict to some special graph class. As width parameters, we consider treewidth, clique-width…