English

Connected covering numbers

Combinatorics 2015-01-14 v3

Abstract

A connected covering is a design system in which the corresponding {\em block graph} is connected. The minimum size of such coverings are called {\em 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 {\em Tur\'an 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.

Keywords

Cite

@article{arxiv.1306.5636,
  title  = {Connected covering numbers},
  author = {Jonathan Chappelon and Kolja Knauer and Luis Pedro Montejano and Jorge Luis Ramírez Alfonsín},
  journal= {arXiv preprint arXiv:1306.5636},
  year   = {2015}
}

Comments

15 pages, 4 figures, 1 table

R2 v1 2026-06-22T00:39:15.639Z