Fractional covers and matchings in families of weighted d-intervals

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F17%3A43932807" target="_blank" >RIV/49777513:23520/17:43932807 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007%2Fs00493-016-3174-7" target="_blank" >https://link.springer.com/article/10.1007%2Fs00493-016-3174-7</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00493-016-3174-7" target="_blank" >10.1007/s00493-016-3174-7</a>

Result language
angličtina
Original language name
Fractional covers and matchings in families of weighted d-intervals
Original language description
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.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA14-19503S" target="_blank" >GA14-19503S: Graph coloring and structure</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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