Stabbing Faces By a Convex Curve

2025/08/24 by Eppstein, David
#Computational Geometry (cs.CG) #FOS: Computer and information sciences

paper · doi:10.48550/arxiv.2508.17549

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.

Citations

• A Note On Universal Point Sets for Planar Graphs
• Drawing Graphs on Few Lines and Few Planes
• On collinear sets in straight line drawings

Related

• Drawing planar graphs of bounded degree with few slopes
• Picking Planar Edges; or, Drawing a Graph with a Planar Subgraph
• Faces in rectilinear drawings of complete graphs
• Drawing Planar Graphs with a Prescribed Inner Face
• Stabbing non-piercing sets and face lengths in large girth plane graphs