DMTCS Proceedings, 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)

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DMTCS Conference vol AE (2005), pp. 161-166


2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)

Stefan Felsner (ed.)

DMTCS Conference Volume AE (2005), pp. 161-166

author: Francisco Javier Zaragoza Martínez
title: The Windy Postman Problem on Series-Parallel Graphs
keywords: windy postman problem, series-parallel graphs, integral polyhedra
abstract: The windy postman problem is the NP-hard problem of finding the minimum cost of a tour traversing all edges of an undirected graph, where the cost of traversal of an edge depends on the direction. Given an undirected graph
, we consider the polyhedron
induced by the linear programming relaxation of a well-known integer programming formulation of the problem. We say that
is windy postman perfect if
is integral. There exists a polynomial-time algorithm, based on the ellipsoid method, to solve the windy postman problem for the class of windy postman perfect graphs. Eulerian graphs and trees are windy postman perfect. By considering a family of polyhedra related to
, we prove that series-parallel graphs are windy postman perfect, therefore solving a conjecture of [Win1987a].
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reference: Francisco Javier Zaragoza Martínez (2005), The Windy Postman Problem on Series-Parallel Graphs, in 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), Stefan Felsner (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AE, pp. 161-166
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