Abstract
Let π 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 π, with respect to one of these linear orders, contains a specified vertex is NP-complete.
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© 2001 Springer-Verlag Berlin Heidelberg
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Puricella, A., Stewart, I.A. (2001). A Generic Greedy Algorithm, Partially-Ordered Graphs and NP-Completeness. In: Brandstädt, A., Le, V.B. (eds) Graph-Theoretic Concepts in Computer Science. WG 2001. Lecture Notes in Computer Science, vol 2204. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45477-2_28
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DOI: https://doi.org/10.1007/3-540-45477-2_28
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