Sink-stable sets of digraphs

Dóra Erdos, A. Frank, Krisztián Kun

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 Thomassé and of Sebo on cyclic stable sets.

Original languageEnglish
Pages (from-to)1651-1674
Number of pages24
JournalSIAM Journal on Discrete Mathematics
Volume28
Issue number4
DOIs
Publication statusPublished - 2014

Fingerprint

Stable Set
Min-max
Digraph
Plane Graph
Theorem
Bipartite Graph
Colouring
Cardinality
Union
Imply

Keywords

  • Clar number
  • Colorations
  • Digraphs
  • Min-max formulae
  • Stable sets

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Sink-stable sets of digraphs. / Erdos, Dóra; Frank, A.; Kun, Krisztián.

In: SIAM Journal on Discrete Mathematics, Vol. 28, No. 4, 2014, p. 1651-1674.

Research output: Contribution to journalArticle

Erdos, Dóra ; Frank, A. ; Kun, Krisztián. / Sink-stable sets of digraphs. In: SIAM Journal on Discrete Mathematics. 2014 ; Vol. 28, No. 4. pp. 1651-1674.
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