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Topology and adjunction in promise constraint satisfaction
arXiv - CS - Discrete Mathematics Pub Date : 2020-03-25 , DOI: arxiv-2003.11351
Andrei Krokhin; Jakub Opršal; Marcin Wrochna; Stanislav Živný

The approximate graph colouring problem concerns colouring a $k$-colourable graph with $c$ colours, where $c\geq k$. This problem naturally generalises to promise graph homomorphism and further to promise constraint satisfaction problems. Complexity analysis of all these problems is notoriously difficult. 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 NP-hardness results for a significant class of approximate graph colouring and promise graph homomorphism problems.
更新日期:2020-03-26

 

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