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

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

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 ∑k i=1 |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...

The Minimum Cy le Cover and the Chinese Postman Problems on Mixed Graphs with Bounded Tree-Width

On Minimum Bisection and Related Partition Problems in Graphs with Bounded Tree Width

Minimum Bisection denotes the NP-hard problem to partition the vertex set of a graph into two sets of equal sizes while minimizing the number of edges between these two sets. We consider this problem in bounded degree graphs with a given tree decomposition (T,X ) and prove an upper bound for their minimum bisection width in terms of the structure and width of (T,X ). When (T,X ) is provided as ...

Parametric Problems on Graphs of Bounded Tree-Width

We consider optimization problems on weighted graphs where vertex and edge weights are polynomial functions of a parameter . We show that, if a problem satis es certain regularity properties and the underlying graph has bounded tree-width, the number of changes in the optimum solution is polynomially bounded. We also show that the description of the sequence of optimum solutions can be construc...

Layout of Graphs with Bounded Tree-Width

A queue layout of a graph consists of a total order of the vertices, and a partition of the edges into queues, such that no two edges in the same queue are nested. The minimum number of queues in a queue layout of a graph is its queue-number. A threedimensional (straight-line grid) drawing of a graph represents the vertices by points in Z and the edges by non-crossing line-segments. This paper ...