Rainbow matchings and cycle-free partial transversals of Latin squares

András Gyárfás, Gábor N. Sárközy

Research output: Article

7 Citations (Scopus)

Abstract

In this paper we show that properly edge-colored graphs G with |V(G)|<4δ(G)-3 have rainbow matchings of size δ(G); this gives the best known bound for a recent question of Wang. We also show that properly edge-colored graphs G with |V(G)|<2δ(G) have rainbow matchings of size at least δ(G)-2δ(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 - júl. 28 2014

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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