One-wasy trail orientation Aamand, Anders; Hjuler, Niklas; Holm, Jacob; Rotenberg, Eva Published in: 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018 DOI: 10.4230/LIPIcs.ICALP.2018.6 Publication date: 2018 Document version Publisher's PDF, also known as Version of record Document license: CC BY Citation for published version (APA): Aamand, A., Hjuler, N., Holm, J., & Rotenberg, E. (2018). One-wasy trail orientation. In C. Kaklamanis, D. Marx, I. Chatzigiannakis, & D. Sannella (Eds.), 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018 [6] Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik. Leibniz International Proceedings in Informatics, LIPIcs Vol. 107 https://doi.org/10.4230/LIPIcs.ICALP.2018.6 Download date: 26. Sep. 2021 One-Way Trail Orientations Anders Aamand1 University of Copenhagen, Copenhagen, Denmark
[email protected] https://orcid.org/0000-0002-0402-0514 Niklas Hjuler2 University of Copenhagen, Copenhagen, Denmark
[email protected] https://orcid.org/0000-0002-0815-670X Jacob Holm3 University of Copenhagen, Copenhagen, Denmark
[email protected] https://orcid.org/0000-0001-6997-9251 Eva Rotenberg4 Technical University of Denmark, Lyngby, Denmark
[email protected] https://orcid.org/0000-0001-5853-7909 Abstract Given a graph, does there exist an orientation of the edges such that the resulting directed graph is strongly connected? Robbins’ theorem [Robbins, Am. Math. Monthly, 1939] asserts that such an orientation exists if and only if the graph is 2-edge connected. A natural extension of this problem is the following: Suppose that the edges of the graph are partitioned into trails. Can the trails be oriented consistently such that the resulting directed graph is strongly connected? We show that 2-edge connectivity is again a sufficient condition and we provide a linear time algorithm for finding such an orientation.