Many sports leagues organize their competitions as round‐robin tournaments. This
tournament design has a rich mathematical structure that has been studied in the literature …

Oneâ•’factorizations of the complete graphâ•flA survey Page 1 One-Factorizations of the
Complete Grapha Survey Eric Mendelsohn" UNIVERSITY OF TORONTO CANADA Alexander …

A permutation array (PA) defined on an r-set of symbols V is av× r array of rows each of
which is a permutation of the symbols of V and such that any two distinct rows have at most …

It is immediate that n must be odd for a Room square of side n to exist. In Figure 1.1 we
present a Room square of side seven. Room squares were named after TG Room who …

A factorization F={F1, F2,..., F} of the graph G is a partition of E (G) into edge-disjoint
spanning subgraphs, F1, F2,..., Fi, called factors.(The factors may contain isolated vertices.) …

The existence of a Room square of order 2 n is known to be equivalent to the existence of
two orthogonal one-factorizations of the complete graph on 2 n vertices, where “orthogonal” …

A Kirkman square with index λ, latinicity μ, block size k, and v points, KS k (v; μ, λ), is at× t
array (t= λ (v− 1)/μ (k− 1)) defined on av-set V such that (1) every point of V is contained in …

Two problems are considered. First, the conjecture that all odd abelian groups except Z 3, Z
5, Z 9, and Z 3+ Z 3 admit strong starters, is reduced to finding strong starters in five types of …

A Howell design of side s and order 2n, or more briefly, an H (s, 2n), is an s× s array in which
each cell either is empty or contains an unordered pair of elements from some 2n-set, say X …

A HILL-CLIMBING ALGORITHM FOR THE CONSTRUCTION OF ONE-FACTORIZATIONS AND
ROOM SQUARES* as follows: choose any YN(X) such that c Page 1 SIAM J. ALG. DISC. METH …