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

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 = { C 1 , … , C k } 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 = 1 k | C i | . 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.