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

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

Local Tree-Width, Excluded Minors, and Approximation Algorithms

The local tree-width of a graph G = (V;E) is the function ltwG : N ! N that associates with every r 2 N the maximal tree-width of an r-neighborhood in G. Our main graph theoretic result is a decomposition theorem for graphs with excluded minors, which says that such graphs can be decomposed into trees of graphs of almost bounded local tree-width. As an application of this theorem, we show that ...

Fair Edge Deletion Problems on Tree- Decomposable Graphs and Improper Colorings

In edge deletion problems, we are given a graph G and a graph property π and the task is to find a subset of edges the deletion of which results in a subgraph of G satisfying the property π. Typically the objective is to minimize the total number of deleted edges, while in less common fair versions the objective is to minimize the maximum number of edges removed from a single vertex. Since many...

Balloons, Chinese Postman Problem and Cycle Double Cover in Cubic Graphs

We previously determined the minimum size of a maximum matching in a connected (2r + 1)-regular graph with n vertices; the extremal graphs have cut-edges. In this paper, we prove a lower bound for the minimum size of a maximum matching in a t-edge-connected r-regular graph with n vertices, for t ≥ 2 and r ≥ 4. The bound is sharp infinitely often and improves a recent result of Henning and Yeo. ...

P6- and triangle-free graphs revisited: structure and bounded clique-width

The MaximumWeight Stable Set (MWS) Problem is one of the fundamental problems on graphs. It is well-known to be NP-complete for triangle-free graphs, and Mosca has shown that it is solvable in polynomial time when restricted to P6and triangle-free graphs. We give a complete structure analysis of (nonbipartite) P6and triangle-free graphs which are prime in the sense of modular decomposition. It ...