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STEPHAN KREUTZER COMPLEXITY OF MODEL-CHECKING PROBLEMS 69/81<br />
INTRODUCTION COMPLEXITY UPPER BOUNDS COMPOSITION LOCALITY LOCALISATION GRIDS GRID-LIKE MINORS LABELLED WEBS<br />
Good Idea, Sadly Wrong<br />
First and wrong proof idea. Use the excluded grid theorem.<br />
Theorem.<br />
(Robertson, Seymour)<br />
There is a computable function f : N → N such that all graphs of<br />
tree-width ≥ f(k) contain a k × k-grid (as a minor).<br />
Proof Idea: given a propositional logic formula w construct G w so that G w<br />
contains |w| 2 ×|w| 2 -grid and proceed as before.<br />
Problem. f(n) := 20 2·k 5<br />
(Robertson, Seymour, Thomas)
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