The approximate graph colouring problem concerns colouring a $k$-colourablegraph with $c$ colours, where $c\geq k$. This problem naturally generalises topromise 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 ofpromise CSPs: one is based on topology and the other on adjunction .

Author(s) : Andrei Krokhin, Jakub Opršal, Marcin Wrochna, Stanislav Živný

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Keywords : adjunction - promise - topology - complexity - problems -

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