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: Candelabra quadruple systems (CQS) were first introduced by Hanani who used them to determine the existence of Steiner quadruple systems. In this paper, a new method has been developed by constructing partial candelabra quadruple systems with odd group size, which is a generalization of the even cases, to complete a design. New results of candelabra quadruple systems have been obtained, i.e. we show that for any , there exists a CQS for all , and .Journal of Combinatorial Designs 09/2014;  [Show abstract] [Hide abstract]
ABSTRACT: Given five positive integers and t where and a tgeneral covering design is a pair where X is a set of n elements (called points) and a multiset of ksubsets of X (called blocks) such that every psubset of X intersects at least λ blocks of in at least t points. In this article we continue the work carried out by Etzion, Wei, and Zhang [Des. Codes Cryptogr. 5 (1995), 217–239] on the asymptotic covering density of general covering designs. We will present combinatorial constructions leading to new upper bounds on the asymptotic covering density of 4(n, 4, 6, 1) general covering designs and 4 general covering designs with . The new bound on the asymptotic covering density of 4(n, 4, 6, 1) general covering designs is equivalent to a new lower bound for the Turán density .Journal of Combinatorial Designs 09/2014;  [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).  [Show abstract] [Hide abstract]
ABSTRACT: A semiframe of type is a GDD of type , , in which the collection of blocks can be written as a disjoint union where is partitioned into parallel classes of and is partitioned into holey parallel classes, each holey parallel class being a partition of for some . A SF is a semiframe of type in which there are p parallel classes in and d holey parallel classes with respect to . In this paper, we shall show that there exists a (3, 1)SF for any if and only if , , , and .Journal of Combinatorial Designs 08/2014;  [Show abstract] [Hide abstract]
ABSTRACT: 2(v,k,1) designs admitting a primitive rank 3 automorphism group , where G0 belongs to the Extraspecial Class, or to the Exceptional Class of Liebeck's Theorem in [23], are classified.Journal of Combinatorial Designs 08/2014;  [Show abstract] [Hide abstract]
ABSTRACT: Latin hypercube designs have been found very useful for designing computer experiments. In recent years, several methods of constructing orthogonal Latin hypercube designs have been proposed in the literature. In this article, we report some more results on the construction of orthogonal Latin hypercubes which result in several new designs.Journal of Combinatorial Designs 08/2014;  [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).  [Show abstract] [Hide abstract]
ABSTRACT: A Gdesign of order n is a decomposition of the complete graph on n vertices into edgedisjoint subgraphs isomorphic to G. Grooming uniform alltoall traffic in optical ring networks with grooming ratio C requires the determination of graph decompositions of the complete graph on n vertices into subgraphs each having at most C edges. The drop cost of such a grooming is the total number of vertices of nonzero degree in these subgraphs, and the grooming is optimal when the drop cost is minimum. The existence spectrum problem of Gdesigns for fivevertex graphs is a long standing problem posed by Bermond, Huang, Rosa and Sotteau in 1980, which is closely related to traffic groomings in optical networks. Although considerable progress has been made over the past 30 years, the existence problems for such Gdesigns and their related traffic groomings in optical networks are far from complete. In this paper, we first give a complete solution to this spectrum problem for fivevertex graphs by eliminating all the undetermined possible exceptions. Then, we determine almost completely the minimum drop cost of 8groomings for all orders n by reducing the 37 possible exceptions to 8. Finally, we show the minimum possible drop cost of 9groomings for all orders n is realizable with 14 exceptions and 12 possible exceptions.Journal of Combinatorial Designs 07/2014; 
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 1factorization of a graph G is a decomposition of G into edgedisjoint 1factors (perfect matchings), and a perfect 1factorization is a 1factorization in which the union of any two of the 1factors is a Hamilton cycle. We consider the problem of the existence of perfect 1factorizations of even order 4regular Cayley graphs, with a particular interest in circulant graphs. In this paper, we study a new family of graphs, denoted , which are Cayley graphs if and only if k is even or . By solving the perfect 1factorization problem for a large class of graphs, we obtain a new class of 4regular bipartite circulant graphs that do not have a perfect 1factorization, answering a problem posed in [7]. With further study of graphs, we prove the nonexistence of P1Fs in a class of 4regular nonbipartite circulant graphs, which is further support for a conjecture made in [7].Journal of Combinatorial Designs 06/2014;  [Show abstract] [Hide abstract]
ABSTRACT: Intersection numbers for subspace designs are introduced and $q$analogs of the Mendelsohn and K\"ohler equations are given. As an application, we are able to determine the intersection structure of a putative $q$analog of the Fano plane for any prime power $q$. It is shown that its existence implies the existence of a $2$$(7,3,q^4)_q$ subspace design. Furthermore, several simplified or alternative proofs concerning intersection numbers of ordinary block designs are discussed.Journal of Combinatorial Designs 05/2014;  [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: 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: 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: In recent years, several methods have been proposed for constructing optimal and minimaxoptimal supersaturated designs (SSDs). However, until now the enumeration problem of such designs has not been yet considered. In this paper, optimal and minimaxoptimal kcirculant SSDs with 6, 10, 14, 18, 22, and 26 runs, factors and are enumerated in a computer search. We have also enumerated all optimal and minimaxoptimal kcirculant SSDs with (mod 4) and . The computer search utilizes the fact that theses designs are equivalent to certain 1rotational resolvable balanced incomplete block designs. Combinatorial properties of these resolvable designs are used to restrict the search space.Journal of Combinatorial Designs 04/2014; 22(4).  [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;
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