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Transversals and multicolored matchings

Akbari, S ; Sharif University of Technology | 2004

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  1. Type of Document: Article
  2. DOI: 10.1002/jcd.20014
  3. Publisher: 2004
  4. Abstract:
  5. Ryser conjectured that the number of transversals of a latin square of order n is congruent to n modulo 2. Balasubramanian has shown that the number of transversals of a latin square of even order is even. A 1-factor of a latin square of order n is a set of n cells no two from the same row or the same column. We prove that for any latin square of order n, the number of 1-factors with exactly n - 1 distinct symbols is even. Also we prove that if the complete graph K2n, n ≥ 8, is edge colored such that each color appears on at most n-2 2e edges, then there exists a multicolored perfect matching. © 2004 Wiley Periodicals, Inc
  6. Keywords:
  7. Latin square ; Multicolored matching ; Transversal
  8. Source: Journal of Combinatorial Designs ; Volume 12, Issue 5 , 2004 , Pages 325-332 ; 10638539 (ISSN)
  9. URL: https://onlinelibrary.wiley.com/doi/abs/10.1002/jcd.20014