3 research outputs found
The travelling preacher, projection, and a lower bound for the stability number of a graph
AbstractThe coflow min鈥搈ax equality is given a travelling preacher interpretation, and is applied to give a lower bound on the maximum size of a set of vertices, no two of which are joined by an edge
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
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鈥檚 coloring theorem. We also exhibit a link to min-max results of Bessy and Thomasse 虂 and of Seb艖 on cyclic stable sets