Homothetic triangle representations of planar graphs
Daniel Gon\c{c}alves, Benjamin L\'ev\^eque, Alexandre Pinlou
TL;DR
This paper proves that every planar graph can be represented as an intersection graph of homothetic triangles, providing a geometric characterization of planar graphs.
Contribution
It introduces a novel geometric representation for all planar graphs using homothetic triangles, expanding understanding of planar graph embeddings.
Findings
Every planar graph admits a homothetic triangle intersection representation
The representation provides new insights into planar graph structure
Potential applications in graph visualization and geometric graph theory
Abstract
We prove that every planar graph is the intersection graph of homothetic triangles in the plane.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Advanced Graph Theory Research · Complexity and Algorithms in Graphs