# Minimal functions on the random graph

@article{Bodirsky2010MinimalFO, title={Minimal functions on the random graph}, author={Manuel Bodirsky and Michael Pinsker}, journal={Israel Journal of Mathematics}, year={2010}, volume={200}, pages={251-296} }

We show that there is a system of 14 non-trivial finitary functions on the random graph with the following properties: Any non-trivial function on the random graph generates one of the functions of this system by means of composition with automorphisms and by topological closure, and the system is minimal in the sense that no subset of the system has the same property. The theorem is obtained by proving a Ramsey-type theorem for colorings of tuples in finite powers of the random graph, and by…

## 39 Citations

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It is proved that either Ψ is contained in one out of 17 classes of graph formulas and the corresponding problem can be solved in polynomial time, or the problem is NP-complete.

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- Mathematics, Computer ScienceICALP
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It is shown that for all structures with domain H_n whose relations are first-order definable in $(H_n,E)$ the constraint satisfaction problem for $\Gamma$ is either in P or is NP-complete, which completes the complexity classification of constraint satisfaction problems of structures first- order definability in countably infinite homogeneous graphs.

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- 2011

It is proved that either Psi is contained in one out of 17 classes of graph formulas and the corresponding problem can be solved in polynomial time, or the problem is NP-complete.

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- 2018

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- Mathematics, Computer ScienceTOCL
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Equations in oligomorphic clones and the Constraint Satisfaction Problem for $ω$-categorical structures

- Mathematics, Computer ScienceJ. Math. Log.
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It is proved that any polymorphism of sufficiently large arity which is totally symmetric modulo outer embeddings of a finitely bounded structure can be turned into a non-trivial system of linear identities, and obtain non-Trivial linear identities for all tractable cases of reducts of the rational order, the random graph, and the random poset.

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