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Quickly excluding a planar graph. (English) Zbl 0807.05023
Summary: In an earlier paper, the first two authors proved that for any planar graph $$H$$, every graph with no minor isomorphic to $$H$$ has bounded tree- width; but the bound given there was enormous. Here we prove a much better bound. We also improve the best known bound on the tree-width of planar graphs with no minor isomorphic to a $$g\times g$$ grid.

##### MSC:
 05C10 Planar graphs; geometric and topological aspects of graph theory 05C35 Extremal problems in graph theory
##### Keywords:
planar graph; minor; bound; tree-width
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