Structural properties of greedoids

Bernhard Korte, László Lovász

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

Greedoids were introduced by the authors as generalizations of matroids providing a framework for the greedy algorithm. In this paper they are studied from a structural aspect. Definitions of basic matroid-theoretical concepts such as rank and closure can be generalized to greedoids, even though they loose some of their fundamental properties. The rank function of a greedoid is only "locally" submodular. The closure operator is not monotone but possesses a (relaxed) Steinitz-McLane exchange property. We define two classes of subsets, called rank-feasible and closure-feasible, so that the rank and closure behave nicely for them. In particular, restricted to rank-feasible sets the rank function is submodular. Finally we show that Rado's theorem on independent transversals of subsets of matroids remains valid for feasible transversals of certain sets of greedoids.

Original languageEnglish
Pages (from-to)359-374
Number of pages16
JournalCombinatorica
Volume3
Issue number3-4
DOIs
Publication statusPublished - Sep 1 1983

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Keywords

  • AMS subject classification (1980): 05B35, 68C05, 15A03

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Computational Mathematics

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