Planar Legendrian graphs
Peter Lambert-Cole, Danielle O'Donnol

TL;DR
This paper classifies trivial Legendrian embeddings of planar graphs in the standard contact 3-sphere, establishing invariants and conditions for Legendrian simplicity, especially for 3-connected graphs or those containing K4 as a minor.
Contribution
It introduces a complete set of invariants for trivial Legendrian embeddings of planar graphs and characterizes when such embeddings are Legendrian simple.
Findings
Oriented Legendrian ribbon and rotation invariant form a complete invariant set.
Unique trivial embedding is Legendrian simple for 3-connected graphs or graphs with K4 minor.
Abstract
We prove two results on the classification of trivial Legendrian embeddings of planar graphs. First, the oriented Legendrian ribbon and rotation invariant are a complete set of invariants. Second, if is 3-connected or contains as a minor, then the unique trivial embedding of is Legendrian simple.
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Taxonomy
TopicsAdvanced Graph Theory Research · Structural Analysis and Optimization · Computational Geometry and Mesh Generation
