A note on transitive orientations with maximum sets of sources and sinks

Authors:
Celina M. H. de Figueiredo;John Gimbel;Célia P. Mello;Jayme L. Szwarcfiter
Affiliations:
Instituto de Matemática and COPPE, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, 21945-970 Rio de Janeiro, RJ, Brazil;Mathematical Sciences, University of Alaska, Fairbanks, Alaska;Instituto de Computação, Universidade Estadual de Campinas, Caixa Postal 6176, 13081-970 Campinas, SP, Brazil;Núcleo de Computação Eletrônica, Instituto de Matemática and COPPE, Universidade Federal do Rio de Janeiro, Caixa Postal 2324, 20001-970 Rio de Janeiro, RJ, Brazil
Venue:
Discrete Applied Mathematics - Sixth Twente Workshop on Graphs and Combinatorial Optimization
Year:
2002

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Abstract

Given a transitive orientation G of a comparability graph G, a vertex of G is a source (sink) if it has indegree (outdegree) zero in G, respectively. A source set of G is a subset of vertices formed by sources of some transitive orientation G. A pair of subsets S, T ⊆ V(G) is a source-sink pair of G when the vertices of S and T are sources and sinks, of some transitive orientation G, respectively. We describe algorithms for finding a transitive orientation with a maximum source-sink pair in a comparability graph. The algorithms are applications of modular decomposition and are all of linear-time complexity.