Mohar's pseudo-triangulation cross-cap drawing conjecture

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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.

References

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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