Research Project: Çizge Tasarımlarında Yapısal Problemler
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Contributors
Funders
ID
TB.00049
Authors
Yazıcı, Emine Şule
Faculty Member
Publications
The number of common flowers of two STS (v)s and embeddable Steiner triple trades
(Elsevier, 2013)
Department of Mathematics
Yes
Yazıcı, Emine Şule
College of Sciences
A flower, F-s(x), around a point x in a Steiner triple system D = (V, B) is the set of all triples in B which contain the point x, namely F-D(X)={b is an element of B vertical bar x is an element of b}. This paper determines the possible number of common flowers that two Steiner triple systems can have in common. For all admissible pairs (k, v) where k <= v-6 we construct a pair of Steiner triple systems of order v where the flowers around k elements of V are identical in both Steiner triple systems, except for the pairs (2, 9), (3, 9) and (6, 13). Equivalently this result shows that there is a Steiner triple trade of foundation I = v k that can be embedded in a STS(v) for each admissible v and 6 <= l <= v except when (l, v) = (6, 9), (7, 9) or (7, 13).
Orthogonal trades and the intersection problem for orthogonal arrays
(Springer Japan Kk, 2016)
Demirkale, Fatih
Donovan, Diane M.
Department of Mathematics
Yes
Küçükçifçi, Selda
This work provides an orthogonal trade for all possible volumes N is an element of Z(+) \ {1, 2, 3, 4, 5, 7} for block size 4. All orthogonal trades of volume N <= 15 are classified up to isomorphism for this block size. The intersection problem for orthogonal arrays with block size 4 is solved for all but finitely many possible exceptions.
A polynomial embedding of pair of partial orthogonal latin squares
(Elsevier, 2014)
Donovan, Diane M.
Department of Mathematics
Yes
Yazıcı, Emine Şule
College of Sciences
We show that a pair of orthogonal partial Latin squares of order n can be embedded in a pair of orthogonal Latin squares of order at most 16n(4) and all orders greater than or equal to 48n(4). This paper provides the first direct polynomial order embedding construction for pairs of orthogonal partial Latin squares.
Maximum uniformly resolvable decompositions of K-v and K-v - I into 3-stars and 3-cycles
(Elsevier, 2015)
Milici, Salvatore
Tuza, Zsolt
Department of Mathematics
Yes
Küçükçifçi, Selda
Let K-v denote the complete graph of order v and K-v - I denote K-v minus a 1-factor. In this article we investigate uniformly resolvable decompositions of K-v and K-v - I into r classes containing only copies of 3-stars and s classes containing only copies of 3-cycles. We completely determine the spectrum in the case where the number of resolution classes of 3-stars is maximum.
Resolvable 3-star designs
(Elsevier, 2015)
Lo Faro, Giovanni
Milici, Salvatore
Tripodi, Antoinette
Department of Mathematics
Yes
Let K-v be the complete graph of order v and F be a set of 1-factors of K-v. In this article we study the existence of a resolvable decomposition of K-v - F into 3-stars when F has the minimum number of 1-factors. We completely solve the case in which F has the minimum number of 1-factors, with the possible exception of v is an element of {40, 44, 52, 76, 92, 100, 280, 284, 328, 332, 428, 472, 476, 572}.