All reports by Author Andrei Krokhin:

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TR20-040
| 25th March 2020
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Andrei Krokhin, Jakub Opršal, Marcin Wrochna, Stanislav Zivny#### Topology and adjunction in promise constraint satisfaction

Revisions: 1

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TR19-053
| 5th April 2019
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Andrei Krokhin, Jakub Opršal#### The complexity of 3-colouring $H$-colourable graphs

Andrei Krokhin, Jakub Opršal, Marcin Wrochna, Stanislav Zivny

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 ...
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Andrei Krokhin, Jakub Opršal

We study the complexity of approximation on satisfiable instances for graph homomorphism problems. For a fixed graph $H$, the $H$-colouring problem is to decide whether a given graph has a homomorphism to $H$. By a result of Hell and Nešet?il, this problem is NP-hard for any non-bipartite graph $H$. In ... more >>>