Connected covering numbers

Abstract : A connected covering is a design system in which the corresponding block graph is connected. The minimum size of such coverings are called connected coverings numbers. In this paper, we present various formulas and bounds for several parameter settings for these numbers. We also investigate results in connection with Turán systems. Finally, a new general upper bound, improving an earlier result, is given. The latter is used to improve upper bounds on a question concerning oriented matroid due to Las Vergnas.
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Submitted on : Tuesday, January 13, 2015 - 10:24:00 AM
Last modification on : Tuesday, May 28, 2019 - 1:54:03 PM
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Jonathan Chappelon, Kolja Knauer, Luis Pedro Montejano, Jorge Luis Ramírez Alfonsín. Connected covering numbers. Journal of Combinatorial Designs, Wiley, 2015, 23 (12), pp.534-549. ⟨10.1002/jcd.21425⟩. ⟨hal-00837648v3⟩

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