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∈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.

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Correspondence to Martin Grohe.

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Grohe, M. Local Tree-Width, Excluded Minors, and Approximation Algorithms. Combinatorica 23, 613–632 (2003). https://doi.org/10.1007/s00493-003-0037-9

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Mathematics Subject Classification (2000):

  • 05C83
  • 05C85
  • 68W25