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.
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Mchedlidze, T., Symvonis, A. (2010). Unilateral Orientation of Mixed Graphs. In: van Leeuwen, J., Muscholl, A., Peleg, D., Pokorný, J., Rumpe, B. (eds) SOFSEM 2010: Theory and Practice of Computer Science. SOFSEM 2010. Lecture Notes in Computer Science, vol 5901. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11266-9_49
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DOI: https://doi.org/10.1007/978-3-642-11266-9_49
Publisher Name: Springer, Berlin, Heidelberg
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