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Generalized covering designs and clique coverings
Author(s) -
Bailey Robert F.,
Burgess Andrea C.,
Cavers Michael S.,
Meagher Karen
Publication year - 2011
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.20288
Subject(s) - mathematics , generalization , clique , combinatorics , class (philosophy) , combinatorial design , discrete mathematics , computer science , artificial intelligence , mathematical analysis
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