Rainbow Matchings and Algebras of Sets

Research output: Contribution to journalArticlepeer-review


Grinblat (Algebras of Sets and Combinatorics, Translations of Mathematical Monographs, vol. 214. AMS, Providence, 2002) asks the following question in the context of algebras of sets: What is the smallest number v= v(n) such that, if A1, … , An are n equivalence relations on a common finite ground set X, such that for each i there are at least v elements of X that belong to Ai-equivalence classes of size larger than 1, then X has a rainbow matching—a set of 2n distinct elements a1, b1, … , an, bn, such that ai is Ai-equivalent to bi for each i? Grinblat has shown that v(n)≤10n/3+O(n). He asks whether v(n) = 3 n- 2 for all n≥ 4. In this paper we improve the upper bound (for all large enough n) to v(n) ≤ 16 n/ 5 + O(1).

Original languageEnglish
Pages (from-to)473-484
Number of pages12
JournalGraphs and Combinatorics
Issue number2
StatePublished - Jan 2017

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


Dive into the research topics of 'Rainbow Matchings and Algebras of Sets'. Together they form a unique fingerprint.

Cite this