Slides.

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