Sink-Stable Sets of Digraphs
Combinatorics
2012-05-29 v1 Discrete Mathematics
Abstract
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.
Cite
@article{arxiv.1205.6071,
title = {Sink-Stable Sets of Digraphs},
author = {Dóra Erdős and András Frank and Krisztián Kun},
journal= {arXiv preprint arXiv:1205.6071},
year = {2012}
}