Slides.

STEPHAN KREUTZER COMPLEXITY OF MODEL-CHECKING PROBLEMS 44/81
INTRODUCTION COMPLEXITY UPPER BOUNDS COMPOSITION LOCALITY LOCALISATION GRIDS GRID-LIKE MINORS LABELLED WEBS
Graph Invariants
Definition:
A graph invariant is a function f : GRAPHS → N.
A class C has bounded f , if there is a constant k : N such that f(G) ≤ k
for all G ∈ C.
Examples:
• f : G ↦→ ∆(G) (max. degree in G)
classes of bounded degree
• f : G ↦→ tw(G) (tree-width of G)
classes of bounded tree-width
• f : G ↦→ mec(G) (mec(G): minimal order of a clique K m ⋠ G)
classes excluding a minor