On Winding Numbers of Almost Embeddings of $$K_4$$ in the Plane
Abstract
Let $$K_4$$ be the complete graph on four vertices. Let $$f$$ be a continuous map of $$K_4$$ to the plane such that $$f$$ -images of nonadjacent edges are disjoint. For any vertex $$v \in K_4$$ take the winding number of the $$f$$ -image of the cycle obtained by deleting $$v$$ (and all adjacent to $$v$$ edges) from $$K_4$$ around $$f(v)$$ . It is known that the sum of these four integers is odd. We construct examples showing that this is the only relation between these four numbers.
Fields of Study & Subjects
Holomorphic and Operator Theory
Point processes and geometric inequalities
Advanced Differential Equations and Dynamical Systems
Publication details
- Journal / source
- Mathematical Notes
- Publisher
- Pleiades Publishing Ltd
- Volume
- 119
- Issue
- 3-4
- Pages
- 367–375
- Publication date
- 1 April 2026
- Language
- EN