14 citations · 78 across the 33 of their papers we have counts for
42 papers
Shuffle automata and the growth of 1324-avoiding permutations
Robert Brignall
We show that . This is achieved by combining the approach of Bevan, Brignall, Elvey Price and Pantone using the `domino', with ideas from…
Chains and unique transitive orientations of prime graphs
Robert Brignall, Sean Mandrick, Vincent Vatter
We give a short, conceptual proof that prime graphs have at most two transitive orientations, a much-quoted result of Gallai. Our proof uses chains, introduced by Chudnovsky, Kim,…
Hereditary pattern-free classes are not always 2-wqo
Robert Brignall
A pattern is a fundamental object used in the proof of Duron, Mählmann and Toruńczyk to show that hereditary 2-wqo graph classes have bounded clique-width. We answer a question in…
Linear clique-width and modular decomposition
Robert Brignall, Michal Opler, Vincent Vatter
A hereditary class of graphs has bounded clique-width if and only if its prime members do, but this lifting property fails for linear clique-width. We prove that a hereditary class…
Pin classes II: Small pin classes
Robert Brignall, Ben Jarvis
Pin permutations play an important role in the structural study of permutation classes, most notably in relation to simple permutations and well-quasi-ordering, and in enumerative…
On cycles in monotone grid classes of permutations
David Bevan, Robert Brignall, Nik Ruškuc
We undertake a detailed investigation into the structure of permutations in monotone grid classes whose row-column graphs do not contain components with more than one cycle. Centra…