224 Tarneaud, P3B 2X1, Sudbury, Ontario, Canada
Horton
J. D.
1981-12
false
Room designs and one-factorizations
en
2019-04-11T12:11
56-63
The existence of a Room square of order 2n is known to be equivalent to the existence of two orthogonal one-factorizations of the complete graph on 2n vertices, where “orthogonal” means “any two one-factors involved have at most one edge in common.” DefineR(n) to be the maximal number of pairwise orthogonal one-factorizations of the complete graph onn vertices. The main results of this paper are bounds on the functionR. If there is a strong starter of order 2n−1 thenR(2n) ≥ 3. If 4n−1 is a prime power, it is shown thatR(4n) ≥ 2n−1. Also, the recursive construction for Room squares, to obtain, a Room design of sidev(u − w) +w from a Room design of sidev and a Room design of sideu with a subdesign of sidew, is generalized to sets ofk pairwise orthogonal factorizations. It is further shown thatR(2n) ≤ 2n−3.
articles
research_article
http://link.springer.com/10.1007%2FBF02190160
1981-12-01
https://scigraph.springernature.com/explorer/license/
0001-9054
1420-8903
Aequationes mathematicae
9dbac06f4cff0bc4874b4bc2c430360ca8a0541208e48b5b019ae19c3a47dd61
readcube_id
Mathematical Sciences
dimensions_id
pub.1033109860
Pure Mathematics
1
22
10.1007/bf02190160
doi
Springer Nature - SN SciGraph project