Journal of Combinatorial Designs (J Combin Des )

Publisher: Wiley InterScience (Online service), John Wiley & Sons


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 t-designs 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 design-theoretic 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.

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    Journal of Combinatorial Designs website
  • Other titles
    Journal of combinatorial designs (Online), Journal of combinatorial designs
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    Document, Periodical, Internet resource
  • Document type
    Internet Resource, Computer File, Journal / Magazine / Newspaper

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John Wiley & Sons

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    • Author can archive a pre-print version
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    • See Wiley-Blackwell entry for articles after February 2007
    • On personal web site or secure external website at authors institution
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    • Articles in some journals can be made Open Access on payment of additional charge
    • 'John Wiley and Sons' is an imprint of 'Wiley-Blackwell'
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    ​ green

Publications in this journal

  • [Show abstract] [Hide abstract]
    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).
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    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).
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    ABSTRACT: A q-ary 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 one-error-correcting () 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 Graeco-Latin cubes.
    Journal of Combinatorial Designs 06/2014;
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    ABSTRACT: A k-cycle 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 k-cycles, the edges of which partition the edges of G. A k-cycle system of is known as a λ-fold k-cycle system of order V. A k-cycle system of (V, C) is said to be enclosed in a k-cycle system of if and . We settle the difficult enclosing problem for λ-fold 5-cycle systems with u = 1.
    Journal of Combinatorial Designs 05/2014; 22(5).
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    ABSTRACT: Squashed 6-cycle systems are introduced as a natural counterpart to 2-perfect 6-cycle systems. The spectrum for the latter has been determined previously in [5]. We determine completely the spectrum for squashed 6-cycle systems, and also for squashed 6-cycle packings.
    Journal of Combinatorial Designs 05/2014; 22(5).
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    ABSTRACT: Every abelian group of even order with a noncyclic Sylow 2-subgroup is known to be R-sequenceable except possibly when the Sylow 2-subgroup has order 8. We construct an R-sequencing for many groups with elementary abelian Sylow 2-subgroups 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 2-groups have terraces. For odd orders it is known that abelian groups are R-sequenceable except possibly those with noncyclic Sylow 3-subgroups. We show how the theory of narcissistic terraces can be exploited to find R-sequencings for many such groups, including infinitely many groups with each possible of Sylow 3-subgroup type of exponent at most 312and all groups whose Sylow 3-subgroups are of the form or .
    Journal of Combinatorial Designs 05/2014;
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    ABSTRACT: A cross-free set of size m in a Steiner triple system is three pairwise disjoint m-element subsets such that no intersects all the three -s. We conjecture that for every admissible n there is an STS(n) with a cross-free set of size which if true, is best possible. We prove this conjecture for the case , constructing an STS containing a cross-free set of size 6k. We note that some of the 3-bichromatic STSs, constructed by Colbourn, Dinitz, and Rosa, have cross-free 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 3-coloring 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 r-colorings as well, if and is a prime power, we show that the answer is the same as in case of complete graphs: in every r-coloring 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;
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    ABSTRACT: A k-star is the complete bipartite graph . Let G and H be graphs, and let be a partial H-decomposition of G. A partial H-decomposition, , of another graph is called an embedding of provided that and G is a subgraph of . We find an embedding of a partial k-star decomposition of into a k-star decomposition of , where s is at most if k is odd, and if k is even.
    Journal of Combinatorial Designs 04/2014; 22(4).
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    ABSTRACT: It is known that extremal ternary self-dual codes of length mod 12) yield 5-designs. Previously, mutually disjoint 5-designs were constructed by using single known generator matrix of bordered double circulant ternary self-dual codes (see [1, 2]). In this paper, a number of generator matrices of bordered double circulant extremal ternary self-dual codes are searched with the aid of computer. Using these codes we give many mutually disjoint 5-designs. As a consequence, a list of 5-spontaneous emission error designs are obtained.
    Journal of Combinatorial Designs 03/2014;
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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 two-part 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).
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    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 1-factorization 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 1-factorization 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;
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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).
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    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;
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    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;
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    ABSTRACT: A 3-uniform friendship hypergraph is a 3-uniform 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 3-uniform friendship hypergraphs on n vertices exist with a so-called universal friend if and only if a Steiner triple system, exists. Hartke and Vandenbussche used integer programming to search for 3-uniform 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 3-uniform friendship hypergraphs. In this paper we construct an infinite family of 3-uniform friendship hypergraphs on 2k vertices and edges. We also construct 3-uniform friendship hypergraphs on 20 and 28 vertices using a computer. Furthermore, we define r-uniform 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 4-uniform friendship hypergraphs with a universal friend. Finally we show how to construct a 4-uniform friendship hypergraph on 9 vertices and with no universal friend.
    Journal of Combinatorial Designs 01/2014;
  • Journal of Combinatorial Designs 12/2013; 21(3-4):127-141.

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