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# Computing 2-walks in polynomial time

Publikationstyp

Journal Article

Publikationsdatum

2018

Sprache

English

TORE-URI

Enthalten in

Volume

14

Start Page

22.1

End Page

22.18

Citation

ACM transactions on algorithms (2018)

Publisher DOI

Publisher

TALG

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, into which the graph is decomposed, are edge-disjoint. This implies the first polynomial-time algorithm that computes the closed 2-walk mentioned above. Its running time is O(n³).

We solve this problem by extending the decomposition of Gao, Richter and Yu in such a way that all pieces, into which the graph is decomposed, are edge-disjoint. This implies the first polynomial-time algorithm that computes the closed 2-walk mentioned above. Its running time is O(n³).