The Z2-Genus of Kuratowski Minors

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10381693" target="_blank" >RIV/00216208:11320/18:10381693 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.4230/LIPIcs.SoCG.2018.40" target="_blank" >https://doi.org/10.4230/LIPIcs.SoCG.2018.40</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4230/LIPIcs.SoCG.2018.40" target="_blank" >10.4230/LIPIcs.SoCG.2018.40</a>

Result language
angličtina
Original language name
The Z2-Genus of Kuratowski Minors
Original language description
An unpublished result by Robertson and Seymour implies that for every t, every graph of sufficiently large genus contains as a minor a projective t x t grid or one of the following so-called t-Kuratowski graphs: K3,t, or t copies of K5 or K3,3 sharing at most 2 common vertices. We show that the Z2-genus of graphs in these families is unbounded in t; in fact, equal to their genus. Together, this implies that the genus of a graph is bounded from above by a function of its Z2-genus, solving a problem posed by Schaefer and Štefankovič, and giving an approximate version of the Hanani-Tutte theorem on orientable surfaces.
Czech name
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Czech description
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
Leibniz International Proceedings in Informatics (LIPIcs)
ISBN
978-3-95977-066-8
ISSN
1868-8969
e-ISSN
neuvedeno
Number of pages
14
Pages from-to
1-14
Publisher name
Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik
Place of publication
Dagstuhl, Germany
Event location
Budapest
Event date
Jun 11, 2018
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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