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arXiv · 2511.09712

Minimal crossing diagrams of spatial graphs

Erica Flapan·Hugh Howards
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Abstract

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.

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Erica Flapan, Hugh Howards. 2025-11-12. Minimal crossing diagrams of spatial graphs. https://arxiv.org/abs/2511.09712

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