Topology and adjunction in promise constraint satisfaction

Andrei Krokhin; Jakub Opršal; Marcin Wrochna; Stanislav Živný

doi:10.1137/20m1378223

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arXiv · 2003.11351

Topology and adjunction in promise constraint satisfaction

Andrei Krokhin·Jakub Opršal·Marcin Wrochna·Stanislav Živný

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Abstract

The approximate graph colouring problem, whose complexity is unresolved in most cases, concerns finding a $c$-colouring of a graph that is promised to be $k$-colourable, where $c\geq k$. This problem naturally generalises to promise graph homomorphism problems and further to promise constraint satisfaction problems. The complexity of these problems has recently been studied through an algebraic approach. In this paper, we introduce two new techniques to analyse the complexity of promise CSPs: one is based on topology and the other on adjunction. We apply these techniques, together with the previously introduced algebraic approach, to obtain new unconditional NP-hardness results for a significant class of approximate graph colouring and promise graph homomorphism problems.

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BibTeX RIS

Andrei Krokhin, Jakub Opršal, Marcin Wrochna, Stanislav Živný. 2020-03-25. Topology and adjunction in promise constraint satisfaction. https://doi.org/10.1137/20m1378223

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