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On the doyen‐wilson theorem for m‐cycle systems
Author(s) -
Bryant Darryn E.,
Rodger C. A.
Publication year - 1994
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.3180020405
Subject(s) - mathematics , generalization , combinatorics , embedding , order (exchange) , discrete mathematics , mathematical analysis , computer science , finance , artificial intelligence , economics
In this article we consider the embedding of m ‐cycle systems of order u in m ‐cycle systems of order v when m is odd. When u and v are 1 or m (mod 2 m ) we completely settle this problem, except possibly for the smallest such embedding in some cases when u ≡ v ≡ m (mod 2 m ). In particular, there are no exceptions if m ∈ {7,9}, so the generalization of the Doyen‐Wilson Theorem is now settled for all odd m with m ≤ 9. © 1994 John Wiley & Sons, Inc.