An Estimate of the Tree-Width of a Planar Graph Which Has Not a Given Planar Grid as a Minor.
We give a more simple than in  proof of the fact that if a finite graph has no minors isomorphic to the planar grid of the size of r × r, then the tree-width of this graph is less than exp(poly(r)). In the case of planar graphs we prove a linear upper bound which improves the quadratic estimate from .
KeywordsPlanar Graph Inductive Condition Combinatorial Theory Connected Subgraph Interior Vertex
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- 2.Diestel, R., Jensen, T.R., Gorbunov, K.Y., Thomassen, C.: Highly connected sets and the excluded grid theorem (Submitted)Google Scholar