Planar Legendrian graphs

2016/04/04 by Peter Lambert‐Cole, Lambert-Cole, Peter, Danielle O’Donnol +1
Computer Science · Engineering · #05C10 #53D10 #57M15 #Advanced Graph Theory Research #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Structural Analysis and Optimization

paper · pdf · doi:10.48550/arxiv.1604.00836

openalex publication_date 2016/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove two results on the classification of trivial Legendrian embeddings g: G → (S³,ξ_std) of planar graphs. First, the oriented Legendrian ribbon R_g and rotation invariant rot_g are a complete set of invariants. Second, if G is 3-connected or contains K₄ as a minor, then the unique trivial embedding of G is Legendrian simple.

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