Journal of Combinatorial Designs (J Combin Des )
Description
The Journal of Combinatorial Designs is an international journal devoted to the timely publication of the most influential papers in the area of combinatorial design theory. All topics in design theory and in which design theory has important applications are covered including: block designs tdesigns pairwise balanced designs and group divisible designs Latin squares quasigroups and related algebras computational methods in design theory construction methods applications in computer science experimental design theory and coding theory graph decompositions factorizations and designtheoretic techniques in graph theory and extremal combinatorics finite geometry and its relation with design theory. algebraic aspects of design theory. Researchers and scientists can depend on the Journal of Combinatorial Designs for the most recent developments in this rapidly growing field and to provide a forum for both theoretical research and applications.
 Impact factor0.69
 5year impact0.63
 Cited halflife8.20
 Immediacy index0.12
 Eigenfactor0.00
 Article influence0.65
 WebsiteJournal of Combinatorial Designs website
 Other titlesJournal of combinatorial designs (Online), Journal of combinatorial designs
 ISSN15206610
 OCLC41616630
 Material typeDocument, Periodical, Internet resource
 Document typeInternet Resource, Computer File, Journal / Magazine / Newspaper
Publisher details
 Preprint
 Author can archive a preprint version
 Postprint
 Author can archive a postprint version
 Conditions
 See WileyBlackwell entry for articles after February 2007
 On personal web site or secure external website at authors institution
 Not allowed on institutional repository
 JASIST authors may deposit in an institutional repository
 Noncommercial
 Preprint must be accompanied with set phrase (see individual journal copyright transfer agreements)
 Published source must be acknowledged with set phrase (see individual journal copyright transfer agreements)
 Publisher's version/PDF cannot be used
 Articles in some journals can be made Open Access on payment of additional charge
 'John Wiley and Sons' is an imprint of 'WileyBlackwell'
 Classification green
Publications in this journal
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ABSTRACT: The notion of a symmetric Hamiltonian cycle system (HCS) of a graph Γ has been introduced and studied by J. Akiyama, M. Kobayashi, and G. Nakamura [J Combin Des 12 (2004), 39–45] for , by R. A. Brualdi and M. W. Schroeder [J Combin Des 19 (2011), 1–15] for , and then naturally extended by V. Chitra and A. Muthusamy [Discussiones Mathematicae Graph Theory, to appear] to the multigraphs and . In each case, there must be an involutory permutation ψ of the vertices fixing all the cycles of the HCS and at most one vertex. Furthermore, for , this ψ should be precisely the permutation switching all pairs of endpoints of the edges of I.An HCS is cyclic if it is invariant under some cyclic permutation of all the vertices. The existence question for a cyclic HCS of has been completely solved by Jordon and Morris [Discrete Math (2008), 2440–2449]—and we note that their cyclic construction is also symmetric for (mod 8). It is then natural to study the existence problem of an HCS of a graph or multigraph Γ as above which is both cyclic and symmetric. In this paper, we completely solve this problem: in the case of even order, the final answer is that cyclicity and symmetry can always cohabit when a cyclic solution exists. On the other hand, imposing that a cyclic HCS of odd order is also symmetric is very restrictive; we prove in fact that an HCS of with both properties exists if and only if is a prime.Journal of Combinatorial Designs 09/2014; 22(9).  [Show abstract] [Hide abstract]
ABSTRACT: Symmetric orthogonal arrays and mixed orthogonal arrays are useful in the design of various experiments. They are also a fundamental tool in the construction of various combinatorial configurations. In this paper, we investigated the mixed orthogonal arrays with four and five factors of strength two, and proved that the necessary conditions of such mixed orthogonal arrays are also sufficient with several exceptions and one possible exception.Journal of Combinatorial Designs 08/2014; 22(8). 
Article: Classification of GraecoLatin Cubes
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ABSTRACT: A qary code of length n, size M, and minimum distance d is called an code. An code with is said to be maximum distance separable (MDS). Here oneerrorcorrecting () MDS codes are classified for small alphabets. In particular, it is shown that there are unique (5, 53, 3)5 and (5, 73, 3)7 codes and equivalence classes of (5, 83, 3)8 codes. The codes are equivalent to certain pairs of mutually orthogonal Latin cubes of order q, called GraecoLatin cubes.Journal of Combinatorial Designs 06/2014;  [Show abstract] [Hide abstract]
ABSTRACT: A kcycle system of a multigraph G is an ordered pair (V, C) where V is the vertex set of G and C is a set of kcycles, the edges of which partition the edges of G. A kcycle system of is known as a λfold kcycle system of order V. A kcycle system of (V, C) is said to be enclosed in a kcycle system of if and . We settle the difficult enclosing problem for λfold 5cycle systems with u = 1.Journal of Combinatorial Designs 05/2014; 22(5).  [Show abstract] [Hide abstract]
ABSTRACT: Squashed 6cycle systems are introduced as a natural counterpart to 2perfect 6cycle systems. The spectrum for the latter has been determined previously in [5]. We determine completely the spectrum for squashed 6cycle systems, and also for squashed 6cycle packings.Journal of Combinatorial Designs 05/2014; 22(5).  [Show abstract] [Hide abstract]
ABSTRACT: Every abelian group of even order with a noncyclic Sylow 2subgroup is known to be Rsequenceable except possibly when the Sylow 2subgroup has order 8. We construct an Rsequencing for many groups with elementary abelian Sylow 2subgroups of order 8 and use this to show that all such groups of order other than 8 also have terraces. This completes the proof of Bailey's Conjecture in the abelian case: all abelian groups other than the noncyclic elementary abelian 2groups have terraces. For odd orders it is known that abelian groups are Rsequenceable except possibly those with noncyclic Sylow 3subgroups. We show how the theory of narcissistic terraces can be exploited to find Rsequencings for many such groups, including infinitely many groups with each possible of Sylow 3subgroup type of exponent at most 312and all groups whose Sylow 3subgroups are of the form or .Journal of Combinatorial Designs 05/2014;  [Show abstract] [Hide abstract]
ABSTRACT: A crossfree set of size m in a Steiner triple system is three pairwise disjoint melement subsets such that no intersects all the three s. We conjecture that for every admissible n there is an STS(n) with a crossfree set of size which if true, is best possible. We prove this conjecture for the case , constructing an STS containing a crossfree set of size 6k. We note that some of the 3bichromatic STSs, constructed by Colbourn, Dinitz, and Rosa, have crossfree sets of size close to 6k (but cannot have size exactly 6k). The constructed STS shows that equality is possible for in the following result: in every 3coloring of the blocks of any Steiner triple system STS(n) there is a monochromatic connected component of size at least (we conjecture that equality holds for every admissible n). The analog problem can be asked for rcolorings as well, if and is a prime power, we show that the answer is the same as in case of complete graphs: in every rcoloring of the blocks of any STS(n), there is a monochromatic connected component with at least points, and this is sharp for infinitely many n.Journal of Combinatorial Designs 04/2014; 
Article: Embedding Partial kStar Designs
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ABSTRACT: A kstar is the complete bipartite graph . Let G and H be graphs, and let be a partial Hdecomposition of G. A partial Hdecomposition, , of another graph is called an embedding of provided that and G is a subgraph of . We find an embedding of a partial kstar decomposition of into a kstar decomposition of , where s is at most if k is odd, and if k is even.Journal of Combinatorial Designs 04/2014; 22(4).  [Show abstract] [Hide abstract]
ABSTRACT: It is known that extremal ternary selfdual codes of length mod 12) yield 5designs. Previously, mutually disjoint 5designs were constructed by using single known generator matrix of bordered double circulant ternary selfdual codes (see [1, 2]). In this paper, a number of generator matrices of bordered double circulant extremal ternary selfdual codes are searched with the aid of computer. Using these codes we give many mutually disjoint 5designs. As a consequence, a list of 5spontaneous emission error designs are obtained.Journal of Combinatorial Designs 03/2014; 
Article: Orientable Hamilton Cycle Embeddings of Complete Tripartite Graphs I: Latin Square Constructions
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ABSTRACT: In an earlier paper the authors constructed a hamilton cycle embedding of in a nonorientable surface for all and then used these embeddings to determine the genus of some large families of graphs. In this twopart series, we extend those results to orientable surfaces for all . In part I, we explore a connection between orthogonal latin squares and embeddings. A product construction is presented for building pairs of orthogonal latin squares such that one member of the pair has a certain hamiltonian property. These hamiltonian squares are then used to construct embeddings of the complete tripartite graph on an orientable surface such that the boundary of every face is a hamilton cycle. This construction works for all such that and for every prime p. Moreover, it is shown that the latin square construction utilized to get hamilton cycle embeddings of can also be used to obtain triangulations of . Part II of this series covers the case for every prime p and applies these embeddings to obtain some genus results.Journal of Combinatorial Designs 02/2014; 22(2).  [Show abstract] [Hide abstract]
ABSTRACT: We prove quadratic upper bounds on the order of any autotopism of a quasigroup or Latin square, and hence also on the order of any automorphism of a Steiner triple system or 1factorization of a complete graph. A corollary is that a permutation σ chosen uniformly at random from the symmetric group will almost surely not be an automorphism of a Steiner triple system of order n, a quasigroup of order n or a 1factorization of the complete graph . Nor will σ be one component of an autotopism for any Latin square of order n. For groups of order n it is known that automorphisms must have order less than n, but we show that quasigroups of order n can have automorphisms of order greater than n. The smallest such quasigroup has order 7034. We also show that quasigroups of prime order can possess autotopisms that consist of three permutations with different cycle structures. Our results answer three questions originally posed by D. Stones.Journal of Combinatorial Designs 02/2014; 
Article: Minimal Kakeya Sets
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ABSTRACT: Blokhuis and Mazzocca (A. Blokhuis and F. Mazzocca, The finite field Kakeya problem (English summary). Building bridges. Bolyai Soc Math Stud 19 (2008) 205–218) provide a strong answer to the finite field analog of the classical Kakeya problem, which asks for the minimum size of a point set in an affine plane π that contains a line in every direction. In this article, we consider the related problem of minimal Kakeya sets, namely Kakeya sets containing no smaller Kakeya sets, and provide an interesting infinite family of minimal Kakeya sets that are not of extremal size.Journal of Combinatorial Designs 02/2014; 22(2).  [Show abstract] [Hide abstract]
ABSTRACT: It is well known that mutually orthogonal latin squares, or MOLS, admit a (Kronecker) product construction. We show that, under mild conditions, `triple products' of MOLS can result in a gain of one square. In terms of transversal designs, the technique is to use a construction of Rolf Rees twice: once to obtain a coarse resolution of the blocks after one product, and next to reorganize classes and resolve the blocks of the second product. As consequences, we report a few improvements to the MOLS table and obtain a slight strengthening of the famous theorem of MacNeish.Journal of Combinatorial Designs 01/2014;  [Show abstract] [Hide abstract]
ABSTRACT: A uniform framework is presented for biembedding Steiner triple systems obtained from the Bose construction using a cyclic group of odd order, in both orientable and nonorientable surfaces. Within this framework, in the nonorientable case, a formula is given for the number of isomorphism classes and the particular biembedding of Ducrocq and Sterboul (preprint 18pp., 1978) is identified. In the orientable case, it is shown that the biembedding of Grannell et al. (J Combin Des 6 (), 325–336) is, up to isomorphism, the unique biembedding of its type. Automorphism groups of the biembeddings are also given.Journal of Combinatorial Designs 01/2014;  [Show abstract] [Hide abstract]
ABSTRACT: A 3uniform friendship hypergraph is a 3uniform hypergraph in which, for all triples of vertices x, y, z there exists a unique vertex w, such that , and are edges in the hypergraph. Sós showed that such 3uniform friendship hypergraphs on n vertices exist with a socalled universal friend if and only if a Steiner triple system, exists. Hartke and Vandenbussche used integer programming to search for 3uniform friendship hypergraphs without a universal friend and found one on 8, three nonisomorphic on 16 and one on 32 vertices. So far, these five hypergraphs are the only known 3uniform friendship hypergraphs. In this paper we construct an infinite family of 3uniform friendship hypergraphs on 2k vertices and edges. We also construct 3uniform friendship hypergraphs on 20 and 28 vertices using a computer. Furthermore, we define runiform friendship hypergraphs and state that the existence of those with a universal friend is dependent on the existence of a Steiner system, . As a result hereof, we know infinitely many 4uniform friendship hypergraphs with a universal friend. Finally we show how to construct a 4uniform friendship hypergraph on 9 vertices and with no universal friend.Journal of Combinatorial Designs 01/2014; 
Article: Flagtransitive pointprimitive symmetric $(\nu ,k,\lambda )$ designs with $\lambda $ at most 100
Journal of Combinatorial Designs 12/2013; 21(34):127141.
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