Abstract
Given a connected graph G, we present a polynomial algorithm which either finds a tour traversing each edge of G exactly two non-consecutive times, one in each direction, or decides that no such tour exists. The main idea of this algorithm is based on the modification of a proof given by Thomassen related to a problem proposed by Ore in 1951.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Benavent, E. and Soler, D. (1998). The Directed Rural Postman Problem with Turn Penalties. Forthcoming inTransportation Science.
Brenner, J.L. and Lindon, B.C. (1984). Doubly Eulerian Trails on Rectangular Grids.Journal of Graph Theory,8, 379–385.
Gabow, H.N. (1976). An efficient implementation of Edmond's algorithm for maximum matching on graphs.J. ACM 23, 221–234.
Gabow, H.N. and Stallman, M. (1986). An Augmenting Path Algorithm for Linear Matroid Parity.Combinatorica 6, 2 123–150.
Lemieux, P.F. and Campagna, L. (1984). The snow ploughing problem solved by a graph theory algorithm.Civil Eng. Systems 1, 337–341.
Ore, O. (1951). A Problem Regarding the Tracing of Graphs.Elem. Math 6, 3 49–53.
Thomassen, C. (1990). Bidirectional Retracting-free Double Tracing and Upper Embeddability of Graphs.Journal of Combinatorial Theory Series B50, 2 198–207.
Troy, D.J. (1966). On Traversing Graphs.Amer. Math. Monthly 73, 497–499.
Xuong, N.H., (1979). How to determine the Maximum Genus of a Graph.Journal of Combinatorial Theory Series B26, 217–225.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
López, E.B., Fernández, D.S. Searching for a strong double tracing in a graph. Top 6, 123–138 (1998). https://doi.org/10.1007/BF02564801
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02564801