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On the existence of a rainbow 1‐factor in 1‐factorizations of K rn ( r )
Author(s) -
ElZanati S.I.,
Plantholt M.J.,
Sissokho P.A.,
Spence L.E.
Publication year - 2007
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.20136
Subject(s) - rainbow , mathematics , combinatorics , factor (programming language) , hypergraph , factorization , physics , algorithm , computer science , quantum mechanics , programming language
Let ${\cal F}$ be a 1‐factorization of the complete uniform hypergraph ${\cal G}={K_{rn}^{(r)}}$ with $r \geq 2$ and $n\geq 3$ . We show that there exists a 1‐factor of ${\cal G}$ whose edges belong to n different 1‐factors in ${\cal F}$ . Such a 1‐factor is called a “rainbow” 1‐factor or an “orthogonal” 1‐factor. © 2007 Wiley Periodicals, Inc. J Combin Designs 15: 487–490, 2007