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Computing 2-Walks in Polynomial Time Schmid, Andreas Schmidt, Jens M. algorithms and data structures 2-walks 3-connected planar graphs Tutte paths 3-trees 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Andreas Schmid and Jens M. Schmidt 2015 Is Part Of LIPIcs, Volume 30, 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2015.676 urn:nbn:de:0030-drops-49502 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.676 eng https://creativecommons.org/licenses/by/3.0/legalcode