2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Stefan Felsner (ed.)
DMTCS Conference Volume AE (2005), pp. 161166
author:  Francisco Javier Zaragoza Martínez 

title:  The Windy Postman Problem on SeriesParallel Graphs 
keywords:  windy postman problem, seriesparallel graphs, integral polyhedra 
abstract: 
The windy postman problem is the NPhard 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
G
, we consider the polyhedron
O(G)
induced by the linear programming relaxation of a
wellknown integer programming formulation of the problem.
We say that
G
is windy postman perfect if
O(G)
is integral. There exists a polynomialtime
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
O(G)
, we prove that seriesparallel 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 SeriesParallel 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. 161166 
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