Connected Covering Numbers

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...

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Bibliographic Details
Published inJournal of combinatorial designs Vol. 23; no. 12; pp. 534 - 549
Main Authors Chappelon, Jonathan, Knauer, Kolja, Montejano, Luis Pedro, Ramírez Alfonsín, Jorge Luis
Format Journal Article
LanguageEnglish
Published Hoboken Blackwell Publishing Ltd 01.12.2015
Wiley Subscription Services, Inc
Wiley
Subjects
5E105
Combinatorics
covering design
Mathematics
Turán-system
uniform-oriented matroidMathematical Subject Classification: 05B05
uniform‐oriented matroidMathematical Subject Classification: 05B05, 5E105
uniform oriented matroid
Turán-system
covering design
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ISSN1063-8539
1520-6610
DOI10.1002/jcd.21425

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Summary: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.
Bibliography:ark:/67375/WNG-7N58FC0Z-K
ArticleID:JCD21425
istex:783C882C0393638A245F611BEF43D2F7CC733499
Contract grant sponsor: ANR TEOMATRO; contract grant number: ANR‐10‐BLAN 0207 (to K.K. and J.L.R.A); contract grant sponsor: CONACYT (L.P.M.).
Dedicated to the memory of Michel Las Vergnas.
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ISSN:1063-8539
1520-6610
DOI:10.1002/jcd.21425