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 on the Clar
number of bipartite plane graphs and a sharpening of Minty's coloring theorem.
We also exhibit a link to min-max results of Bessy and Thomasse and of Sebo on
cyclic stable sets