We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Durham University

Computer Science


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


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.