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STEPHAN KREUTZER COMPLEXITY OF MODEL-CHECKING PROBLEMS 50/81<br />
INTRODUCTION COMPLEXITY UPPER BOUNDS COMPOSITION LOCALITY LOCALISATION GRIDS GRID-LIKE MINORS LABELLED WEBS<br />
Localisation of Graph Invariants<br />
Theorem: First-order model checking is fixed-parameter tractable on<br />
• planar graphs (Frick, Grohe 01)<br />
• graphs of locally bounded tree-width (Frick, Grohe 01)<br />
Theorem: (Flum, Grohe 01)<br />
First-order model-checking is fixed-parameter tractable on graph classes<br />
excluding a minor.<br />
Theorem: (Dawar, Grohe, K. 07)<br />
First-order model-checking is fixed-parameter tractable on graph classes<br />
locally excluding a minor.<br />
Theorem: (Dvořák, Kral, Thomas 11)<br />
First-order model-checking is fixed-parameter tractable on graph classes<br />
of locally bounded expansion.
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