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Küçükçifçi, Selda

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Now showing 1 - 10 of 36
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    On regular embedding of H-designs into G-designs
    (Utilitas Mathematica, 2013) Quattrocchi, Gaetano; Department of Mathematics; Department of Mathematics; Department of Mathematics; Küçükçifçi, Selda; Smith, Benjamin R.; Yazıcı, Emine Şule; Faculty Member; Researcher; Faculty Member; Department of Mathematics; College of Sciences; College of Sciences; College of Sciences; 105252; N/A; 27432
    The graph H is embedded in the graph G, if H is a subgraph of G. An H-design is a decomposition of a complete graph into edge disjoint copies of the graph H, called blocks. An H-i-design with k blocks, say H-1, H-2, ...H-k is embedded in a G-design if for every H-i, there exists a distinct block, say G(i), in the G-design that embeds H-i. If G(i) are all isomorphic for 1 <= i <= k then the embedding is called regular. This paper solves the problem of the regular embedding of H-designs into G-designs when G has at most four vertices and four edges.
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    Orthogonal trades and the intersection problem for orthogonal arrays
    (Springer Japan Kk, 2016) Demirkale, Fatih; Donovan, Diane M.; Department of Mathematics; Department of Mathematics; Küçükçifçi, Selda; Yazıcı, Emine Şule; Faculty Member; Faculty Member; Department of Mathematics; College of Sciences; College of Sciences; 105252; 27432
    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.
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    Decomposition of lambda K-nu into kites and 4-cycles
    (Charles Babbage Research Centre, 2017) Milici, Salvatore; Department of Mathematics; Küçükçifçi, Selda; Faculty Member; Department of Mathematics; College of Sciences; 105252
    Given a collection of graphs H, an H-decomposition of λkv is a decomposition of the edges of λKv into isomorphic copies of graphs in Ti. A kite is a triangle with a tail consisting of a single edge. In this paper we investigate the decomposition problem when H is the set containing a kite and a 4-cycle, that is; this paper gives a complete solution to the problem of decomposing λKv into r kites and s 4-cycles for every admissible values of v, λ, r and s.
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    Embedding 4-cycle systems into octagon triple systems
    (2009) Billington, Elizabeth J.; Lindner, Curt; Department of Mathematics; Department of Mathematics; Küçükçifçi, Selda; Yazıcı, Emine Şule; Faculty Member; Faculty Member; Department of Mathematics; College of Sciences; College of Sciences; 105252; 27432
    An octagon triple is the graph consisting of the four triangles (triples) {a, b,c}, {c, d,e}, {e, f,g}, and {g, h,a}, where a,b,c, d,e, f, g and h axe distinct. The 4-cycle (a, c, e, g) is called an inside 4-cycle. An octagon triple system of order n is a pair (X,O), where O is a collection of edge disjoint octagon triples which partitions the edge set of K-n with vertex set X. Let (X, O) be an octagon triple system and let P be the collection of inside 4-cycles. Then (X, P) is a partial 4-cycle system of order n. It is not possible for (X, P) to be a 4-cycle system (not enough 4-cycles). So the problem of determining for each n the smallest octagon triple system whose inside 4-cycles contain a 4-cycle system of order 8n + 1 is immediate. The object of this note is to determine the spectrum for octagon triple systems and to construct for every n a 4-cycle system of order k = 8n + 1 that can be embedded in the inside 4-cycles of some octagon triple system of order approximately 3k. This is probably not the best possible embedding (the best embedding is approximately 2k + 1), but it is a good start.
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    The full metamorphosis of lambda-fold block designs with block size four into lambda-fold kite systems
    (Utilitas Mathematica Publishing, 2013) N/A; Department of Mathematics; Department of Mathematics; Department of Mathematics; Küçükçifçi, Selda; Smith, Benjamin R.; Yazıcı, Emine Şule; Faculty Member; Researcher; Faculty Member; Department of Mathematics; College of Sciences; College of Sciences; College of Sciences; 105252; N/A; 27432
    Let(X,B)be a λ-fold block design with block size 4. If a path of length two is removed from each block of B the resulting collection of kites K is a partial λ-fold kite system(X,K). If the deleted edges can be arranged into a collection of kites D,then(X,K ∪ D)is a λ-fold kite system [5]. Now for each block 6 ∈ B let {P1(6),P 2(b),P3(b)} be a partition of b into paths of length two and define for each i = 1,2,3, sets Ki and Di as follows: for each b ∈ B,put the kite b\Pi(b)in Ki and the two edges belonging to the path Pi(b)in Di. If the edges in Di can be arranged into a collection of kites Di * then Mi =(X,Ki∪Di *)is a λ-fold kite system,called the ith metamorphosis of(X,B). The full metamorphosis is the set of three metamorphoses {M 1,M2,M3}. We give a complete solution of the following problem: for which n and A does there exist a λ-fold block design with block size 4 having a full metamorphosis into a λ-fold kite system?
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    The metamorphosis of lambda-fold block designs with block size four into maximum packings of lambda K-n with kites
    (Util Math Publ Inc, 2005) N/A; Department of Mathematics; Küçükçifçi, Selda; Faculty Member; Department of Mathematics; College of Sciences; 105252
    Let (X, B) be a lambda-fold block design with block size four and define sets B(K) and E(K-4 \ K) as follows: for each block b is an element of B, remove a path of length two, obtain a kite (a triangle with a tail), and place the kites in B(K) and the paths of length 2 in E(K-4 \ K). If we can reassemble the edges belonging to E(K-4 \ K) into a collection of kites E(K) with leave L, then (X, B(K) boolean OR E(K), L) is a packing of lambda K-n with kites. If vertical bar L vertical bar is as small as possible, then (X, B(K) boolean OR E(K), L) is called a metamorphosis of the lambda-fold block design (X, B) into a maximum packing of lambda K-n with kites. In this paper we give a complete solution of the metamorphosis problem for lambda-fold block designs with block size four into a maximum packing of lambda K-n with kites for all lambda. That is, for each lambda we determine the set of all n such that there exists a lambda-fold block design of order n having a metamorphosis into a maximum packing of lambda K-n with kites.
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    The full metamorphosis of λ-fold block designs with block size four into A-fold 4-cycle systems
    (Charles Babbage Res Ctr, 2012) Lindner, Charles Curtis; Department of Mathematics; Department of Mathematics; Küçükçifçi, Selda; Yazıcı, Emine Şule; Faculty Member; Faculty Member; Department of Mathematics; College of Sciences; College of Sciences; 105252; 27432
    Let (X, B) be a lambda-fold block design with block size 4. If a pair of disjoint edges are removed from each block of B the resulting collection of 4-cycles C is a partial lambda-fold 4-cycle system (X, C). If the deleted edges can be arranged into a collection of 4-cycles D, then (X,C boolean OR D) is a lambda-fold 4-cycle system [10]. Now for each block b is an element of B specify a 1-factorization of b as {F-1(b), F-2(b), F-3(b)} and define for each i = 1,2,3, sets C-i and D-i as follows: for each b is an element of B, put the 4-cycle b backslash F-i(b) in C-i and the 2 edges belonging to F-i(b) in D-i. If the edges in D-i can be arranged into a collection of 4-cycles D-i* then M-i = (X, C-i boolean OR D-i*) is a lambda-fold 4-cycle system, called the ith metamorphosis of (X, B). The full metamorphosis is the set of three metamorphoses {M-1, M-2, M-3}. We give a complete solution of the following problem: for which n and lambda does there exist a lambda-fold block design with block size 4 having a full metamorphosis into a lambda-fold 4-cycle system?
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    The metamorphosis of λ-fold block designs with block size four into maximum packings of λkn with kites
    (Utilitas Mathematica Academy, 2005) N/A; Department of Mathematics; Küçükçifçi, Selda; Faculty Member; Department of Mathematics; College of Sciences; 105252
    Let (X, B) be a λ-fold block design with block size four and define sets B(K) and E(K4\ K) as follows: for each block b ε B, remove a path of length two, obtain a kite (a triangle with a tail), and place the kites in B(K) and the paths of length 2 in E(K4\ K). If we can reassemble the edges belonging to E(K4\ K) into a collection of kites E(K) with leave L, then (X, B(K) ∪ E(K), L) is a packing of λK n with kites. If |L| is as small as possible, then (X, B(K) ∪ E(K), L) is called a metamorphosis of the λ-fold block design (X, B) into a maximum packing of λKn with kites. In this paper we give a complete solution of the metamorphosis problem for λ-fold block designs with block size four into a maximum packing of λKn with kites for all λ. That is, for each λ we determine the set of all n such that there exists a λ-fold block design of order n having a metamorphosis into a maximum packing of λKn with kites.
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    Cyles in 2-factorizations of Kn
    (Anadolu Üniversitesi, 2002) N/A; Department of Mathematics; Küçükçifçi, Selda; Faculty Member; Department of Mathematics; College of Sciences; 105252
    This work studies cycles in 2-faetorizations of K n (undireeted complete graph with n vertices) and gives a complete solution (with three possible exceptions) of the problem of constructing 2-factorizations of K n containing a specified number of 8-cycles, for both n even and odd. / Bu çalışmada n köşeli tam graflardaki döngüler problemi işlenmekte, tek ve çift köşeli tam graflardaki 8-döngü sayısı problemine (üç olası istisna ile) çözüm verilmektedir.
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    The full metamorphosis of λ-fold block designs with block size four into λ-fold triple systems
    (Charles Babbage Research Centre, 2012) Lindner, Curt; Department of Mathematics; Department of Mathematics; Yazıcı, Emine Şule; Küçükçifçi, Selda; Faculty Member; Faculty Member; Department of Mathematics; College of Sciences; College of Sciences; 27432; 105252
    Let (X, B) be a λ-fold block design with block size 4. If a star is removed from each block of B the resulting collection of triangles T is a partial λ-fold triple system (X, T). If the edges belonging to the deleted stars can be arranged into a collection of triangles S, then (X,T ∪ S) is a λ-fold triple system, called a metamorphosis of the A-fold block design (X, B) into a λ-fold triple system. Label the elements of each block b with b 1,b 2,b 3, and b 4 (in any manner). For each i = 1,2,3,4 define a set of triangles T iand a set of stars S i as follows: for each block b = [b 1,b 2,b 3,b 4] belonging to B, partition b into a triangle and a star centered at b i, and place the triangle in T i and the star in S i. Then (X, T i) is a partial λ-fold triple system. Now if the edges belonging to the stars in S i can be arranged into a collection of triangles S i, then (X, T i ∪ S i) is a λ-fold triple system and we say that M i = (X, T i∪S i) is the ith metamorphosis of (X, B). The full metamorphosis of (X, B) is the set of four metamorphoses {M 1, M 2, M 3, M 4}. The purpose of this work is to give a complete solution of the following problem: For which n and λ does there exist a λ-fold block design with block size 4 having a full metamorphosis into λ-fold triple systems? Copyright © 2012, Charles Babbage Research Centre All rights reserved.