Generalized covering designs and clique coverings |
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| Authors: | Robert F Bailey Andrea C Burgess Michael S Cavers Karen Meagher |
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| Institution: | 1. Department of Mathematics and Statistics, University of Regina, 3737 Wascana Parkway, Regina, SK, S4S 0A2 Canada;2. Department of Mathematics, Ryerson University, 350 Victoria St., Toronto, ON, M5B 2K3 Canada;3. Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, AB, T2N 1N4 Canada |
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| Abstract: | Inspired by the “generalized t‐designs” defined by Cameron P. J. Cameron, Discrete Math 309 (2009), 4835–4842], we define a new class of combinatorial designs which simultaneously provide a generalization of both covering designs and covering arrays. We then obtain a number of bounds on the minimum sizes of these designs, and describe some methods of constructing them, which in some cases we prove are optimal. Many of our results are obtained from an interpretation of these designs in terms of clique coverings of graphs. © 2011 Wiley Periodicals, Inc. J Combin Designs 19:378‐406, 2011 |
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| Keywords: | covering design covering array generalized covering design clique covering |
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