Unilateral Orientation of Mixed Graphs

Authors:
Tamara Mchedlidze;Antonios Symvonis
Affiliations:
Dept. of Mathematics, National Technical University of Athens, Athens, Greece;Dept. of Mathematics, National Technical University of Athens, Athens, Greece
Venue:
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
Year:
2009

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Abstract

A digraph D is unilateral if for every pair x, y of its vertices there exists a directed path from x to y, or a directed path from y to x, or both. A mixed graph M = (V,A,E) with arc-set A and edge-set E accepts a unilateral orientation, if its edges can be oriented so that the resulting digraph is unilateral. In this paper, we present the first linear-time recognition algorithm for unilaterally orientable mixed graphs. Based on this algorithm we derive a polynomial algorithm for testing whether a unilaterally orientable mixed graph has a unique unilateral orientation.