Title:	Fractional covers and matchings in families of weighted d-intervals
Authors:	Aharoni, Ron Kaiser, Tomáš Zerbib, Shira
Citation:	AHARONI, R., KAISER, T., ZERBIB, S. Fractional covers and matchings in families of weighted d-intervals. Combinatorica>, 2017, roč. 37, č. 4, s. 555-572. ISSN 0209-9683.
Issue Date:	2017
Publisher:	Springer Verlag
Document type:	preprint preprint
URI:	http://hdl.handle.net/11025/29281
ISSN:	0209-9683
Keywords:	d-interval;odpovídající číslo;příčné číslo
Keywords in different language:	d-interval;matching number;transversal number
Abstract in different language:	A d-interval is a union of at most d disjoint closed intervals on a fixed line. Tardos [Combinatorica 15 (1995), 123-134] and the second author [Disc. Comput. Geom. 18 (1997), 195-203] used topological tools to bound the transversal number τ of a family H of d-intervals in terms of d and the matching number ν of H. We investigate the weighted and fractional versions of this problem and prove upper bounds that are tight up to constant factors. We apply both the topological method and an approach of Alon [Disc. Comput. Geom. 19 (1998), 333-334]. For the use of the latter, we prove a weighted version of Turan's theorem. We also provide a proof of the second author's upper bound that is more direct than the original proof.
Rights:	© Springer Verlag
Appears in Collections:	Články / Articles (KMA) Preprinty / Preprints (KMA) OBD

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