Geodesic
On minimal strongly connected congruences of a directed path
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 6 (2006) no. 1, pp. 91-95.

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Let $G = (V, \alpha)$ be a directed graph. An equivalence relation $\theta\subseteq V\times V$ is called a strongly connected congruence of $G$ if the quotient graph $G/\theta$ is strongly connected. Minimal (under inclusion) strongly connected congruences of a directed path are described and the total amount of them is found ($2^{n-3}$ if the path has $n$ vertices). 
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M. R. Mirzayanov. On minimal strongly connected congruences of a directed path. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 6 (2006) no. 1, pp. 91-95. http://geodesic.mathdoc.fr/item/ISU_2006_6_1_a10/

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