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On the logical complexity of convex polygon dissections

Manuel Bodirsky·Mihyun Kang·Oleg Verbitsky
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Abstract

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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Manuel Bodirsky, Mihyun Kang, Oleg Verbitsky. 2006-07-21. On the logical complexity of convex polygon dissections. https://arxiv.org/abs/math/0607531

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