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Local tree-width, excluded minors, and approximation algorithms

Martin Grohe
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Abstract

The local tree-width of a graph G=(V,E) is the function ltw^G: N -> N that associates with every natural number r the maximal tree-width of an r-neighborhood in G. Our main graph theoretic result is a decomposition theorem for graphs with excluded minors that essentially says that such graphs can be decomposed into trees of graphs of bounded local tree-width. As an application of this theorem, we show that a number of combinatorial optimization problems, such as 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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Martin Grohe. 2000-01-24. Local tree-width, excluded minors, and approximation algorithms. https://arxiv.org/abs/math/0001128

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