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Durham University

Computer Science

Profile

Publication details for Professor Iain Stewart

Puricella, A. & Stewart, I.A. (2001). A generic greedy algorithm, partially-ordered graphs and NP-completeness. 27th International Workshop on Graph-Theoretic Concepts in Computer Science, WG'01, Rostock, Germany, Springer-Verlag.

Author(s) from Durham

Abstract

Let $\pi$ be any fixed polynomial-time testable, non-trivial, hereditary property of graphs. Suppose that the vertices of a graph G are not necessarily linearly ordered but partially ordered, where we think of this partial order as a collection of (possibly exponentially many) linear orders in the natural way. We prove that the problem of deciding whether a lexicographically first maximal subgraph of G satisfying $\pi$, with respect to one of these linear orders, contains a specified vertex is NP-complete.