Stabbing Faces By a Convex Curve

We prove that, for every plane graph $G$ and every smooth convex curve $C$ not on a single line, there exists a straight-line drawing of $G$ for which every face is crossed by $C$.

Publication Details

Journal
ArXiv.org
Published
2025-08-24
Primary Topic
Geochemistry and Geologic Mapping
Type
article
Field-Weighted Citation Impact
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article

Stabbing Faces By a Convex Curve

ArXiv.org
Geochemistry and Geologic Mapping
article

Stabbing Faces By a Convex Curve

article en

Abstract

We prove that, for every plane graph $G$ and every smooth convex curve $C$ not on a single line, there exists a straight-line drawing of $G$ for which every face is crossed by $C$.

ArXiv.org
Openalex Percentile: Top 64%
Geochemistry and Geologic Mapping
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Stabbing Faces By a Convex Curve · ArXiv.org (2025) | TGRS Research Map | TGRS