2025/11/12 by Erica Flapan, Flapan, Erica, Hugh Howards +1
Computer Science · Engineering · #05C10 #57K10 #57M15 #Advanced Graph Theory Research #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Structural Analysis and Optimization
paper · pdf · doi:10.48550/arxiv.2511.09712
openalex publication_date 2025/11/12 · openalex created_date 2025/11/15 · openalex updated_date 2026/07/28
We prove that all 1-vertex spatial graphs with adequate diagrams have minimal crossing number, and that spatial graph diagrams obtained by replacing vertices and edges of a planar embedded graph by minimal crossing link or spatial graph diagrams have minimal crossing number. Finally, we give an example in answer to a question of Adams et al. about minimal crossing diagrams of rigid vertex graphs.