Let F0 be a fixed k-uniform hypergraph. The problem of finding the integer F0-packing number Î½F0(H) of a k-uniform hypergraph H is an NP-hard problem. Finding the fractional F0-packing number Î½âˆ—â€¦ (More)

We introduce a new general polynomial-time constructionthe fibre constructionwhich reduces any constraint satisfaction problem CSP(H) to the constraint satisfaction problem CSP(P), where P is anyâ€¦ (More)

Given a graph H , let b(H) be the minimum integer b, if it exists, for which H -colouring is N P-complete when restricted to instances with degree bounded by b. We show that b(H) exists for anyâ€¦ (More)

We further generalise a construction â€“ the fibre construction â€“ that was developed in an earlier paper of the first two authors. The extension in this paper gives a polynomial-time reduction ofâ€¦ (More)

In this note, we present a new proof of the H-colouring Dichotomy, which was proved by Hell and NeÅ¡etÅ™il in 1990, and was reproved by Bulatov in 2005. The proof is much shorter than the originalâ€¦ (More)

We investigate the class of reflexive graphs that admit semilattice polymorphisms, and in doing so, give an algebraic characterisation of chordal graphs. In particular, we show that a graph G isâ€¦ (More)

Classical results of Birkhoff and of Dilworth yield an extremely useful representation of a finite distributive lattice L as the downset lattice D(JL) of poset JL of join-irreducible elements of L.â€¦ (More)

We describe a generating set for the variety of simple graphs that admit a k-ary near-unanimity polymorphism. The result follows from an analysis of NU polymorphisms of strongly bipartite digraphs,â€¦ (More)