Tag Archives: graph

Graph isomorphism

Fix an \omega-categorical structure \atoms. The simplest, and already interesting case is (\mathbb N,=), the pure countable set.

We consider the definable graph isomorphism problem for graphs which are definable (equivalently, interpret in) \atoms:

Problem: DefGraphIso

Input: Two definable graphs G,H

Output: Yes, if G and H are isomorphic, No otherwise.

Below we make some very basic observations concerning this problem.

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