Elsevier

Discrete Applied Mathematics

Volume 157, Issue 2, 28 January 2009, Pages 272-279
Discrete Applied Mathematics

Minimum cycle cover and Chinese postman problems on mixed graphs with bounded tree-width

https://doi.org/10.1016/j.dam.2007.10.032Get rights and content
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Abstract

Let M=(V,E,A) be a mixed graph with vertex set V, edge set E and arc set A. A cycle cover of M is a family C={C1,,Ck} of cycles of M such that each edge/arc of M belongs to at least one cycle in C. The weight of C is i=1k|Ci|. The minimum cycle cover problem is the following: given a strongly connected mixed graph M without bridges, find a cycle cover of M with weight as small as possible. The Chinese postman problem is: given a strongly connected mixed graph M, find a minimum length closed walk using all edges and arcs of M. These problems are NP-hard. We show that they can be solved in polynomial time if M has bounded tree-width.

Keywords

Tree-width
Polynomial algorithms
Cycle cover
Chinese postman problem
Mixed graphs

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