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STEPHAN KREUTZER COMPLEXITY OF MODEL-CHECKING PROBLEMS 70/81<br />

INTRODUCTION COMPLEXITY UPPER BOUNDS COMPOSITION LOCALITY LOCALISATION GRIDS GRID-LIKE MINORS LABELLED WEBS<br />

Grid-Like Minors<br />

We will therefore use grid-like minors instead of grids.<br />

Theorem.<br />

(Reed, Wood)<br />

Any graph G of tree-width ≥ k 5 contains two sets P,Q of disjoint paths<br />

such that their intersection graph I(P,Q) contains a K k -minor.

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