One-wasy trail orientation
Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
Documents
- OA-One-wasy trail orientation
Final published version, 448 KB, PDF document
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 su cient condition and we provide a linear time algorithm for finding such an orientation. The generalised Robbins' theorem [Boesch, Am. Math. Monthly, 1980] for mixed multigraphs asserts that the undirected edges of a mixed multigraph can be oriented to make the resulting directed graph strongly connected exactly when the mixed graph is strongly connected and the underlying graph is bridgeless. We consider the natural extension where the undirected edges of a mixed multigraph are partitioned into trails. It turns out that in this case the condition of the generalised Robbin's Theorem is not su cient. However, we show that as long as each cut either contains at least 2 undirected edges or directed edges in both directions, there exists an orientation of the trails such that the resulting directed graph is strongly connected. Moreover, if the condition is satisfied, we may start by orienting an arbitrary trail in an arbitrary direction. Using this result one obtains a very simple polynomial time algorithm for finding a strong trail orientation if it exists, both in the undirected and the mixed setting.
Original language | English |
---|---|
Title of host publication | 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018 |
Editors | Christos Kaklamanis, Daniel Marx, Ioannis Chatzigiannakis, Donald Sannella |
Number of pages | 13 |
Publisher | Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik |
Publication date | 1 Jul 2018 |
Article number | 6 |
ISBN (Electronic) | 9783959770767 |
DOIs | |
Publication status | Published - 1 Jul 2018 |
Event | 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018 - Prague, Czech Republic Duration: 9 Jul 2018 → 13 Jul 2018 |
Conference
Conference | 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018 |
---|---|
Land | Czech Republic |
By | Prague |
Periode | 09/07/2018 → 13/07/2018 |
Sponsor | Avast, RSJ |
Series | Leibniz International Proceedings in Informatics, LIPIcs |
---|---|
Volume | 107 |
ISSN | 1868-8969 |
- Graph algorithms, Graph orientation, Robbins' theorem
Research areas
Number of downloads are based on statistics from Google Scholar and www.ku.dk
ID: 230343849