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arXiv · 2309.17121

Face sizes and the connectivity of the dual

Gunnar Brinkmann·Kenta Noguchi·Heidi Van den Camp
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Abstract

For each $c\ge 1$ we prove tight lower bounds on face sizes that must be present to allow $1$- or $2$-cuts in simple duals of $c$-connected maps. Using these bounds, we determine the smallest genus on which a $c$-connected map can have a simple dual with a $2$-cut and give lower and some upper bounds for the smallest genus on which a $c$-connected map can have a simple dual with a $1$-cut.

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Gunnar Brinkmann, Kenta Noguchi, Heidi Van den Camp. 2023-10-31. Face sizes and the connectivity of the dual. https://arxiv.org/abs/2309.17121

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