conference paper published yes Radoslav Fulek author 39F3FFE4-F248-11E8-B48F-1D18A9856A870000-0001-8485-1774 Jan Kynčl author UlWa department SoCG: Symposium on Computational Geometry Eliminating intersections in drawings of graphs project 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of a graph G is the minimum g such that G has an independently even drawing on the orientable surface of genus g. An unpublished result by Robertson and Seymour implies that for every t, every graph of sufficiently large genus contains as a minor a projective t × t grid or one of the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 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. Schloss Dagstuhl - Leibniz-Zentrum für Informatik2018Budapest, Hungary eng 1803.0508510.4230/LIPIcs.SoCG.2018.40 9940.1 - 40.14 https://research-explorer.ista.ac.at/record/11593 Fulek, R., &#38; Kynčl, J. (2018). The ℤ2-Genus of Kuratowski minors (Vol. 99, p. 40.1-40.14). Presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href="https://doi.org/10.4230/LIPIcs.SoCG.2018.40">https://doi.org/10.4230/LIPIcs.SoCG.2018.40</a> Fulek, Radoslav, and Jan Kynčl. <i>The ℤ2-Genus of Kuratowski Minors</i>. Vol. 99, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 40.1-40.14, doi:<a href="https://doi.org/10.4230/LIPIcs.SoCG.2018.40">10.4230/LIPIcs.SoCG.2018.40</a>. R. Fulek and J. Kynčl, “The ℤ2-Genus of Kuratowski minors,” presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary, 2018, vol. 99, p. 40.1-40.14. Fulek R, Kynčl J. 2018. The ℤ2-Genus of Kuratowski minors. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 99, 40.1-40.14. Fulek R, Kynčl J. The ℤ2-Genus of Kuratowski minors. In: Vol 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2018:40.1-40.14. doi:<a href="https://doi.org/10.4230/LIPIcs.SoCG.2018.40">10.4230/LIPIcs.SoCG.2018.40</a> R. Fulek, J. Kynčl, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 40.1-40.14. Fulek, Radoslav, and Jan Kynčl. “The ℤ2-Genus of Kuratowski Minors,” 99:40.1-40.14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. <a href="https://doi.org/10.4230/LIPIcs.SoCG.2018.40">https://doi.org/10.4230/LIPIcs.SoCG.2018.40</a>. 1862018-12-11T11:45:05Z2025-04-14T13:52:37Z