Abstract:In 1982, Berge defined the class of $\alpha$-diperfect digraphs. A digraph $D$ is $\alpha$-diperfect if every induced subdigraph of $H$ of $D$ satisfies the following property: for every maximum stable set $S$ of $H$ there is a path partition $\mathcal{P}$ of $H$ in which every $P \in \mathcal{P}$ contains exactly one vertex of $S$. Berge conjectured a characterization of $\alpha$-diperfect digraphs by forbidding induced orientations of odd cycles. In 2018, Sambinelli, Nunes da Silva and Lee proposed a similar… Show more
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