We show that approximate graph colouring is not solved by constantly many levels of the lift-
and-project hierarchy for the combined basic linear programming and affine integer …

We study the power of the bounded-width consistency algorithm in the context of the fixed-
template Promise Constraint Satisfaction Problem (PCSP). Our main technical finding is that …

We show that approximate graph colouring is not solved by any level of the affine integer
programming (AIP) hierarchy. To establish the result, we translate the problem of exhibiting …

We provide a unified framework to study hierarchies of relaxations for Constraint Satisfaction
Problems and their Promise variant. The idea is to split the description of a hierarchy into an …

The Weisfeiler-Leman (WL) dimension of a graph parameter $ f $ is the minimum $ k $ such
that, if $ G_1 $ and $ G_2 $ are indistinguishable by the $ k $-dimensional WL-algorithm …

A query algorithm based on homomorphism counts is a procedure for determining whether a
given instance satisfies a property by counting homomorphisms between the given instance …

In a recent line of work, Butti and Dalmau have shown that a fixed-template Constraint
Satisfaction Problem is solvable by a certain natural linear programming relaxation …

A graph parameter is a function f on graphs with the property that, for any pair of isomorphic
graphs G1 and G2, f (G1)= f (G2). The Weisfeiler--Leman (WL) dimension of f is the minimum …

In this paper we study the interactions between so-called fractional relaxations of the integer
programs (IPs) which encode homomorphism and isomorphism of relational structures. We …

Game comonads represent a rare application of category theoretic methods to the fields of
finite model theory and descriptive complexity. First introduced by Abramsky, Dawar and …