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arXiv · 2304.09647

Face-simple minimal quadrangulations of surfaces

Sarah Abusaif·Warren Singh·Timothy Sun
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Abstract

For each surface besides the sphere, projective plane, and Klein bottle, we construct a face-simple minimal quadrangulation, i.e., a simple quadrangulation on the fewest number of vertices possible, whose dual is also a simple graph. Our result answers a question of Liu, Ellingham, and Ye while providing a simpler proof of their main result. The inductive construction is based on an earlier idea for finding near-quadrangular embeddings of the complete graphs using the diamond sum operation.

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Sarah Abusaif, Warren Singh, Timothy Sun. 2023-05-22. Face-simple minimal quadrangulations of surfaces. https://arxiv.org/abs/2304.09647

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