Combinatorica

, Volume 23, Issue 4, pp 613–632

Local Tree-Width, Excluded Minors, and Approximation Algorithms

Original Paper

DOI: 10.1007/s00493-003-0037-9

Cite this article as:
Grohe, M. Combinatorica (2003) 23: 613. doi:10.1007/s00493-003-0037-9

The local tree-width of a graph G=(V,E) is the function ltwG :ℕ→ℕ that associates with every r∈ℕ the maximal tree-width of an r-neighborhood in G. Our main grapht heoretic 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 a number of combinatorial optimization problems, suchas Minimum Vertex Cover, Minimum Dominating Set, and Maximum Independent Set have a polynomial time approximation scheme when restricted to a class of graphs with an excluded minor.

Mathematics Subject Classification (2000):

05C8305C8568W25

Copyright information

© János Bolyai Mathematical Society 2003

Authors and Affiliations

  1. 1.Humboldt-Universität zu Berlin, Institut für InformatikBerlinGermany