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Publication details for Professor Iain Stewart

Puricella, A. & Stewart, I.A. (2003). Greedy algorithms, H-colourings and a complexity-theoretic dichotomy. Theoretical Computer Science 290(3): 1897-1913.

• Publication type: Journal papers: academic
• ISSN/ISBN: 0304-3975
• DOI: 10.1016/S0304-3975(02)00329-8
• Keywords: Computational complexity, Constraint satisfaction, Graph algorithms, Dicotomies.
• View online: Online version
• Durham research online: DRO record

Author(s) from Durham

• Professor Iain Stewart

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.