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# Computing 2-walks in polynomial time

Publikationstyp

Conference Paper

Publikationsdatum

2015-03

TORE-URI

First published in

Number in series

30

Start Page

676

End Page

688

Citation

32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015) 30: 676-688 (2015)

Contribution to Conference

Publisher DOI

Scopus ID

Publisher

Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH, Dagstuhl Publishing

© 2015 LIPICS. A 2-walk of a graph is a walk visiting every vertex at least once and at most twice. By generalizing decompositions of Tutte and Thomassen, Gao, Richter and Yu proved that every 3-connected planar graph contains a closed 2-walk such that all vertices visited twice are contained in 3-separators. This seminal result generalizes Tutte's theorem that every 4-connected planar graph is Hamiltonian as well as Barnette's theorem that every 3-connected planar graph has a spanning tree with maximum degree at most 3. The algorithmic challenge of finding such a closed 2-walk is to overcome big overlapping subgraphs in the decomposition, which are also inherent in Tutte's and Thomassen's decompositions. We solve this problem by extending the decomposition of Gao, Richter and Yu in such a way that all pieces, in which the graph is decomposed into, are edge-disjoint. This implies the first polynomial-time algorithm that computes the closed 2-walk mentioned above.