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Computing 2-walks in polynomial time
Publikationstyp
Conference Paper
Date Issued
2015-03
Author(s)
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.
Subjects
2-walks
3-connected planar graphs
3-trees
Algorithms and data structures
Tutte paths