Mohar's pseudo-triangulation cross-cap drawing conjecture

Let gg be a positive integer, and let NgN_g be the non-orientable surface of genus gg. A loopless pseudo-triangulation of NgN_g is a cellularly embedded loopless multigraph in which every face has degree three. A perfect cross-cap drawing has gg cross-caps and every edge intersects each cross-cap at most once. Mohar's pseudo-triangulation conjecture. Every loopless pseudo-triangulation of NgN_g admits a perfect cross-cap drawing. The paper explicitly states that this stronger conjecture is disproved by Schaefer and Štefankovič, so it is not an open problem.

Sources & referencesView supporting material

Primary source

Niloufar Fuladi, Alfredo Hubard and Arnaud de Mesmay, “Degenerate crossing number and signed reversal distance”, arXiv:2308.10666 (2025).

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