Abstract
Since its definition in 1944, the concept of kernel of a digraph has been thoroughly studied. It has many applications in game theory, mathematical logic and other branches of mathematics. In this paper we establish a bijection between digraphs and square hypergraphs with a (fixed) system of distinct representatives, which allows us to obtain new results on kernels of digraphs. Among them, we prove a modification of a well-known conjecture by Meyniel.
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