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STEPHAN KREUTZER COMPLEXITY OF MODEL-CHECKING PROBLEMS 46/81<br />
INTRODUCTION COMPLEXITY UPPER BOUNDS COMPOSITION LOCALITY LOCALISATION GRIDS GRID-LIKE MINORS LABELLED WEBS<br />
Bounded Local Tree-Width<br />
Bounded local tree-width:<br />
f : G ↦→ tw(G) tree-width of graphs<br />
{ (<br />
loc f (G, r) := max tw G [ N r (v) ]) }<br />
: v ∈ V(G)<br />
Example: Every class of graphs of bounded degree has bounded local<br />
tree-width.<br />
Example: The class of planar graphs has bounded local tree-width.<br />
Theorem:<br />
Every planar graph of diameter r has tree-width at most 3r.<br />
(Baker)
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