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# Greedy algorithms, H-colourings and a complexity-theoretic dichotomy.

Puricella, A. and Stewart, I. A. (2003) 'Greedy algorithms, H-colourings and a complexity-theoretic dichotomy.', Theoretical computer science., 290 (3). pp. 1897-1913.

## Abstract

Let H be a fixed undirected graph. An H-colouring of an undirected graph G is a homomorphism from G to H. If the vertices of G are partially ordered then there is a generic non-deterministic greedy algorithm which computes all lexicographically first maximal H-colourable subgraphs of G. We show that the complexity of deciding whether a given vertex of G is in a lexicographically first maximal H-colourable subgraph of G is NP-complete, if H is bipartite, and ${\bf \Sigma}_2^p$-complete, if H is non-bipartite. This result complements Hell and Nesetril's seminal dichotomy result that the standard H-colouring problem is in P, if H is bipartite, and NP-complete, if H is non-bipartite. Our proofs use the basic techniques established by Hell and Nesetril, combinatorially adapted to our scenario.

Item Type: Article Computational complexity, Constraint satisfaction, Graph algorithms, Dicotomies. PDF - Accepted Version (258Kb) Peer-reviewed http://dx.doi.org/10.1016/S0304-3975(02)00329-8 10 Oct 2008 14 Jun 2011 16:31

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