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C. R. J. Clapham 《Periodica Mathematica Hungarica》1987,18(4):317-318
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An optimal holey packing OHPd(2, k, n, g) is equivalent to a maximal (g + 1)‐ary (n, k, d) constant weight code. In this paper, we provide some recursive constructions for OHPd(2, k, n, g)'s and use them to investigate the existence of an OHP4(2, 4, n, 3) for n ≡ 2, 3 (mod 4). Combining this with Wu's result ( 18 ), we prove that the necessary condition for the existence of an OHP4(2, 4, n, 3), namely, n ≥ 5 is also sufficient, except for n ∈ {6, 7} and except possibly for n = 26. © 2005 Wiley Periodicals, Inc. J Combin Designs 14: 111–123, 2006 相似文献
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Patric R. J. Östergård 《Designs, Codes and Cryptography》2002,27(3):257-260
The smallest BIBD, as for the number of points and blocks, whose existence is still undecided is 2-(22, 8, 4). Possible subconfigurations of such a design, namely 2-(10, 4, 4) designs, are here ruled out. The result is obtained by classifying all 2-(10, 4, 4) designs and trying to find 2-(22, 8, 4) designs by solving instances of the maximum clique problem. 相似文献
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Quasi-symmetric designs are block designs with two block intersection numbersx andy It is shown that with the exception of (x, y)=(0, 1), for a fixed value of the block sizek, there are finitely many such designs. Some finiteness results on block graphs are derived. For a quasi-symmetric 3-design
with positivex andy, the intersection numbers are shown to be roots of a quadratic whose coefficients are polynomial functions ofv, k and λ. Using this quadratic, various characterizations of the Witt—Lüneburg design on 23 points are obtained. It is shown
that ifx=1, then a fixed value of λ determines at most finitely many such designs. 相似文献
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Mieko Yamada 《Journal of Combinatorial Theory, Series A》1979,27(3):378-381
Hadamard matrices of the Williamson type invariant under an automorphism of order 2 are considered. A new Hadamard matrix of order 148 of this type is obtained. 相似文献
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Trevor J. Gionet Jr. Erika L.C. King Yixiao Sha 《Discrete Applied Mathematics》2011,159(12):1225-1230
In 1995, Plummer (1992) [6] published a paper in which he gave a characterization of 4-regular, 4-connected, claw-free graphs. Based on that work, Hartnell and Plummer (1996) [5] published a paper on 4-connected, claw-free, well-covered graphs a year later. However, in his 1995 paper, Plummer inadvertently omitted some of the graphs with odd order. In this paper, we will complete Plummer’s characterization of all 4-connected, 4-regular, claw-free graphs, and then show the implications this has on the well-covered graphs he and Hartnell determined. In addition, we will characterize 4-connected, 4-regular, claw-free, well-dominated graphs. 相似文献
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For given graphs , , the -color Ramsey number, denoted by , is the smallest integer such that if we arbitrarily color the edges of a complete graph of order with colors, then it always contains a monochromatic copy of colored with , for some . Let be a cycle of length and a star of order . In this paper, firstly we give a general upper bound of . In particular, for the 3-color case, we have and this bound is tight in some sense. Furthermore, we prove that for all and , and if is a prime power, then the equality holds. 相似文献
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Variations of the trade-off method exist in the literature of design theory and have been utilized by some authors to produce some t-designs with or without repeated blocks. In this paper we explore a new version of this algorithmic method (i) to produce 20 nonisomorphic and rigid 4-(12,5,4) designs, (ii) to study the spectrum of support sizes of 4-(12,5,4) designs. Along these, we also present a new design invariant for testing isomorphism among designs and a new way of representing t-designs. 相似文献
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Periodica Mathematica Hungarica - 相似文献
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