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The Existence of (K 2 × K 6)-Designs

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Abstract

Direct and recursive constructions are established for graph designs for K 2 × K 6 grid-blocks. Using these, the existence of graph designs of index one in which the blocks are K 2 × K 6 grid-blocks is completely determined: A (K 2 × K 6)-design of order v exists if and only if \({v\equiv1\pmod{72}}\).

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Authors and Affiliations

  1. School of Science, Jiangnan University, Wuxi, 214122, China

    Chengmin Wang

  2. School of Computing Informatics and Decision Systems Engineering, Arizona State University, Tempe, AZ, 85287-8809, USA

    Charles J. Colbourn

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  1. Chengmin Wang
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  2. Charles J. Colbourn
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Correspondence to Chengmin Wang.

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Wang, C., Colbourn, C.J. The Existence of (K 2 × K 6)-Designs. Graphs and Combinatorics 29, 1557–1567 (2013). https://doi.org/10.1007/s00373-012-1187-6

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  • DOI: https://doi.org/10.1007/s00373-012-1187-6

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