Hanani-Tutte for approximating maps of graphs

Abstract

We resolve in the affirmative conjectures of A. Skopenkov and Repovš (1998), and M.

Skopenkov (2003) generalizing the classical Hanani-Tutte theorem to the setting of approximating maps of graphs on 2-dimensional surfaces by embeddings.

Keywords

• Hanani–Tutte theorem
• graph embedding
• map approximation
• weak embedding
• clustered planarity