On the existence of a rainbow 1‐factor in 1‐factorizations of  K        rn    (  r  ) | Zendy

ElZanati S.I. | Zendy; Plantholt M.J. | Zendy; Sissokho P.A. | Zendy; Spence L.E. | Zendy

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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

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