Labelled well-quasi-order for permutation classes

Well-Quasi-Order for Permutation Graphs Omitting a Path and a Clique

We consider well-quasi-order for classes of permutation graphs which omit both a path and a clique. Our principle result is that the class of permutation graphs omitting P5 and a clique of any size is well-quasi-ordered. This is proved by giving a structural decomposition of the corresponding permutations. We also exhibit three infinite antichains to show that the classes of permutation graphs ...

A well-quasi-order for tournaments

A digraph H is immersed in a digraph G if the vertices of H are mapped to (distinct) vertices of G, and the edges of H are mapped to directed paths joining the corresponding pairs of vertices of G, in such a way that the paths are pairwise edge-disjoint. For graphs the same relation (using paths instead of directed paths) is a well-quasi-order; that is, in every infinite set of graphs some one ...

Exact unprovability results for compound well-quasi-ordered combinatorial classes

In this paper we prove general exact unprovability results that show how a threshold between provability and unprovability of a finite well-quasi-orderedness assertion of a combinatorial class is transformed by the sequence-construction, multisetconstruction, cycle-construction and labeled-tree-construction. Provability proofs use asymptotic pigeonhole principle, unprovability proofs use Weierm...

Grid classes and partial well order

We prove necessary and sufficient conditions on a family of (generalised) gridding matrices to determine when the corresponding permutation classes are partially well-ordered. One direction requires an application of Higman’s Theorem and relies on there being only finitely many simple permutations in the only non-monotone cell of each component of the matrix. The other direction is proved by a ...

Well-Quasi-Order of Relabel Functions