Forskning ved Københavns Universitet - Københavns Universitet

Forside

One-wasy trail orientation

Publikation: Bidrag til bog/antologi/rapportKonferencebidrag i proceedingsForskningfagfællebedømt

Dokumenter

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.

OriginalsprogEngelsk
Titel45th International Colloquium on Automata, Languages, and Programming, ICALP 2018
RedaktørerChristos Kaklamanis, Daniel Marx, Ioannis Chatzigiannakis, Donald Sannella
Antal sider13
ForlagSchloss Dagstuhl--Leibniz-Zentrum fuer Informatik
Publikationsdato1 jul. 2018
Artikelnummer6
ISBN (Elektronisk)9783959770767
DOI
StatusUdgivet - 1 jul. 2018
Begivenhed45th International Colloquium on Automata, Languages, and Programming, ICALP 2018 - Prague, Tjekkiet
Varighed: 9 jul. 201813 jul. 2018

Konference

Konference45th International Colloquium on Automata, Languages, and Programming, ICALP 2018
LandTjekkiet
ByPrague
Periode09/07/201813/07/2018
SponsorAvast, RSJ
NavnLeibniz International Proceedings in Informatics, LIPIcs
Vol/bind107
ISSN1868-8969

ID: 230343849