5 papers
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 ToruÅczyk to show that hereditary 2-wqo graph classes have bounded clique-width. We answer a question i…
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…
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…
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…
Uncountably many enumerations of well-quasi-ordered permutation classes
Robert Brignall, Vincent Vatter
We construct an uncountable family of well-quasi-ordered permutation classes, each with a distinct enumeration sequence. This disproves a conjecture that all well-quasi-ordered per…