
TL;DR
This paper proves that for any plane graph and any smooth convex curve not on a line, there exists a straight-line drawing where the curve crosses every face, revealing a new geometric property of plane graphs.
Contribution
It introduces a universal construction showing that any plane graph can be drawn so that a convex curve intersects all faces, a novel geometric insight.
Findings
Existence of such a drawing for all plane graphs
Construction method for the straight-line drawing
Implications for geometric graph theory
Abstract
We prove that, for every plane graph and every smooth convex curve not on a single line, there exists a straight-line drawing of for which every face is crossed by .
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