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Connected Covering Numbers
Author(s) -
Chappelon Jonathan,
Knauer Kolja,
Montejano Luis Pedro,
Ramírez Alfonsín Jorge Luis
Publication year - 2015
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.21425
Subject(s) - upper and lower bounds , matroid , combinatorics , mathematics , connection (principal bundle) , graph , connectivity , discrete mathematics , block (permutation group theory) , connected component , computer science , geometry , mathematical analysis
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.