Covering with latin transversals

Noga Alon, Joel Spencer, Prasad Tetali

Research output: Contribution to journalArticle

Abstract

Given an n × n matrix A = [aij], a transversal of A is a set of elements, one from each row and one from each column. A transversal is a latin transversal if no two elements are the same. Erdös and Spencer showed that there always exists a latin transversal in any n × n matrix in which no element appears more than s times, for s≤ (n - 1)/16. Here we show that, in fact, the elements of the matrix can be partitioned into n disjoint latin transversals, provided n is a power of 2 and no element appears more than εn times for some fixed ε>0. The assumption that n is a power of 2 can be weakened, but at the moment we are unable to prove the theorem for all values of n.

Original languageEnglish (US)
Pages (from-to)1-10
Number of pages10
JournalDiscrete Applied Mathematics
Volume57
Issue number1
DOIs
StatePublished - Feb 10 1995

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Transversals
Covering
Disjoint
Moment
Theorem

ASJC Scopus subject areas

  • Applied Mathematics
  • Discrete Mathematics and Combinatorics

Cite this

Covering with latin transversals. / Alon, Noga; Spencer, Joel; Tetali, Prasad.

In: Discrete Applied Mathematics, Vol. 57, No. 1, 10.02.1995, p. 1-10.

Research output: Contribution to journalArticle

Alon, Noga ; Spencer, Joel ; Tetali, Prasad. / Covering with latin transversals. In: Discrete Applied Mathematics. 1995 ; Vol. 57, No. 1. pp. 1-10.
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