Year: 2006
Type: preprint
Abstract: Given a finite cover f:tilde{G} \to G and an embedding of tilde{G} in the plane, Negami conjectures that G embeds in P^2. Negami proved this conjecture for regular covers. In this paper we define two properties (Propserties V and E), depending on the cover tilde{G} and its embedding into S^2, and generalize Negami's result by showing: (1) If Properties V and E are fulfilled then G embeds in P^2. (2) Regular covers always fulfill Properties V and E. We give an example of an irregular cover fulfilling Properties V and E. Covers not fulfilling Properties V and E are discussed as well.
Source: arXiv (Cornell University)
Authors: Rieck, Yo'av, Yamashita, Yasushi
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W50379056