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 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. 
D\'ora Erd\H{o}s, Andr\'as Frank and Kriszti\'an Kun
math.CO cs.DM