Surjective H-Colouring: New Hardness Results
Abstract
A homomorphism from a graph G to a graph H is a vertex mapping f from the vertex set of G to the vertex set of H such that there is an edge between vertices f(u) and f(v) of H whenever there is an edge between vertices u and v of G. The H-Colouring problem is to decide whether or not a graph G allows a homomorphism to a fixed graph H. We continue a study on a variant of this problem, namely the Surjective H-Colouring problem, which imposes the homomorphism to be vertex-surjective. We build upon previous results and show that this problem is NP-complete for every connected graph H that has exactly two vertices with a self-loop as long as these two vertices are not adjacent. As a result, we can classify the computational complexity of Surjective H-Colouring for every graph H on at most four vertices.
Keywords
Cite
@article{arxiv.1701.02188,
title = {Surjective H-Colouring: New Hardness Results},
author = {Petr Golovach and Matthew Johnson. Barnaby Martin and Daniel Paulusma and Anthony Stewart},
journal= {arXiv preprint arXiv:1701.02188},
year = {2017}
}