On the logical complexity of convex polygon dissections

Details On the logical complexity of convex polygon dissections On the logical complexity of convex polygon dissections

2006-07-21

arxiv.org/abs/math/0607531v1

Mathematics

Combinatorics

26 pages

Scientific paper

The logical depth of a graph $G$ is the minimum quantifier depth of a first order sentence defining $G$ up to isomorphism in the language of the adjacency and the equality relations. We consider the case that $G$ is a dissection of a convex polygon or, equivalently, a biconnected outerplanar graph. We bound the logical depth of a such $G$ from above by a function of combinatorial parameters of the dual tree of $G$.

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