Finding Tutte Paths in Linear Time

Authors Therese Biedl , Philipp Kindermann

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Author Details

Therese Biedl
  • David R. Cheriton School of Computer Science, University of Waterloo, Canada
Philipp Kindermann
  • Lehrstuhl für Informatik I, Universität Würzburg, Germany

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Therese Biedl and Philipp Kindermann. Finding Tutte Paths in Linear Time. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 23:1-23:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


It is well-known that every planar graph has a Tutte path, i.e., a path P such that any component of G-P has at most three attachment points on P. However, it was only recently shown that such Tutte paths can be found in polynomial time. In this paper, we give a new proof that 3-connected planar graphs have Tutte paths, which leads to a linear-time algorithm to find Tutte paths. Furthermore, our Tutte path has special properties: it visits all exterior vertices, all components of G-P have exactly three attachment points, and we can assign distinct representatives to them that are interior vertices. Finally, our running time bound is slightly stronger; we can bound it in terms of the degrees of the faces that are incident to P. This allows us to find some applications of Tutte paths (such as binary spanning trees and 2-walks) in linear time as well.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • planar graph
  • Tutte path
  • Hamiltonian path
  • 2-walk
  • linear time


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