Sink-Stable Sets of Digraphs

We introduce the notion of sink-stable sets of a digraph and prove a min-max formula for the maximum cardinality of the union of k sink-stable sets. The results imply a recent min-max theorem of Abeledo and Atkinson [1] on the Clar number of bipartite plane graphs and a sharpening of Minty’s coloring theorem [18]. We also exhibit a link to min-max results of Bessy and Thomassé [3] and of Sebő [19] on cyclic stable sets.