---
res:
bibo_abstract:
- 'A drawing of a graph on a surface is independently even if every pair of nonadjacent
edges in the drawing crosses an even number of times. The Z2 -genus of a graph
G is the minimum g such that G has an independently even drawing on the orientable
surface of genus g. An unpublished result by Robertson and Seymour implies that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×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 two 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. We
also obtain an analogous result for Euler genus and Euler Z2-genus of graphs.@eng'
bibo_authorlist:
- foaf_Person:
foaf_givenName: Radoslav
foaf_name: Fulek, Radoslav
foaf_surname: Fulek
foaf_workInfoHomepage: http://www.librecat.org/personId=39F3FFE4-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0001-8485-1774
- foaf_Person:
foaf_givenName: Jan
foaf_name: Kynčl, Jan
foaf_surname: Kynčl
bibo_doi: 10.1007/s00454-022-00412-w
bibo_volume: 68
dct_date: 2022^xs_gYear
dct_identifier:
- UT:000825014500001
dct_isPartOf:
- http://id.crossref.org/issn/0179-5376
- http://id.crossref.org/issn/1432-0444
dct_language: eng
dct_publisher: Springer Nature@
dct_title: The Z2-Genus of Kuratowski minors@
...