Rainbow matchings and cycle-free partial transversals of Latin squares

A. Gyárfás, Gábor N. Sárközy

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

In this paper we show that properly edge-colored graphs G with |V(G)|G)2/3. This result extends (with a weaker error term) the well-known result that a factorization of the complete bipartite graph Kn,n has a rainbow matching of size n-o(n), or equivalently that every Latin square of order n has a partial transversal of size n-o(n) (an asymptotic version of the Ryser-Brualdi conjecture). In this direction we also show that every Latin square of order n has a cycle-free partial transversal of size n-o(n).

Original languageEnglish
Pages (from-to)96-102
Number of pages7
JournalDiscrete Mathematics
Volume327
Issue number1
DOIs
Publication statusPublished - Jul 28 2014

Fingerprint

Transversals
Magic square
Factorization
Partial
Cycle
Edge-colored Graph
Complete Bipartite Graph
Error term

Keywords

  • Partial transversals in Latin squares
  • Proper edge colorings
  • Rainbow matchings

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Rainbow matchings and cycle-free partial transversals of Latin squares. / Gyárfás, A.; Sárközy, Gábor N.

In: Discrete Mathematics, Vol. 327, No. 1, 28.07.2014, p. 96-102.

Research output: Contribution to journalArticle

Gyárfás, A. ; Sárközy, Gábor N. / Rainbow matchings and cycle-free partial transversals of Latin squares. In: Discrete Mathematics. 2014 ; Vol. 327, No. 1. pp. 96-102.
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