A Generic Greedy Algorithm, Partially-Ordered Graphs and NP-Completeness

Authors:
Antonio Puricella;Iain A. Stewart
Affiliations:
-;-
Venue:
WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science
Year:
2001

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Abstract

Let 驴 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 驴, with respect to one of these linear orders, contains a specified vertex is NP-complete.