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Electronic Colloquium on Computational Complexity

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Reports tagged with graph homomorphism:
TR14-163 | 29th November 2014
Arnaud Durand, Meena Mahajan, Guillaume Malod, Nicolas de Rugy-Altherre, Nitin Saurabh

Homomorphism polynomials complete for VP

The VP versus VNP question, introduced by Valiant, is probably the most important open question in algebraic complexity theory. Thanks to completeness results, a variant of this question, VBP versus VNP, can be succinctly restated as asking whether the permanent of a generic matrix can be written as a determinant ... more >>>

TR19-053 | 5th April 2019
Andrei Krokhin, Jakub Opršal

The complexity of 3-colouring $H$-colourable graphs

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 >>>

TR20-040 | 25th March 2020
Andrei Krokhin, Jakub Opršal, Marcin Wrochna, Stanislav Zivny

Topology and adjunction in promise constraint satisfaction

Revisions: 1

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 ... more >>>

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