eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2015-02-26
676
688
10.4230/LIPIcs.STACS.2015.676
article
Computing 2-Walks in Polynomial Time
Schmid, Andreas
Schmidt, Jens M.
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol030-stacs2015/LIPIcs.STACS.2015.676/LIPIcs.STACS.2015.676.pdf
algorithms and data structures
2-walks
3-connected planar graphs
Tutte paths
3-trees