Given a digraph \(D=(V(D),A(D))\) , a set S of vertices of D is a kernel of D if it satisfies that: (i) for \( u,v\in S\) , \( (u,v) \notin A(D)\) and (ii) for every \(u \in V(D)\setminus S\) , there exists \(v \in S\) , such that \((u,v) \in A(D)\) . One of the most important results about kernels in digraphs is the following one, due to M. Richardson: Every digraph with no odd cycles has a kernel. The work and history of Graph Theory in Mexico is deeply woven with the study of kernels in digraphs and, particularly, with the work on Richardson’s theorem along with several generalizations of this result. In this paper, we provide a thorough review of this result and its generalizations.
