Euler´s Formula for General Graph Embeddings
Ponente: Linda Lesniak
Institución: Western Michigan University
Tipo de Evento: Investigación
Institución: Western Michigan University
Tipo de Evento: Investigación
| Cuándo |
25/11/2025 de 17:00 a 18:00 |
|---|---|
| Dónde | Aula teórica, Unidad Juriquilla |
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The ancient Greeks knew that there are exactly five regular polyhedra. And in each of these, we have the identity that the number of vertices minus the number of edges plus the number of faces is 2. Many generalizations of this formula have been discovered by mathematicians over the centuries.
The general graph theory version of this theorem, known as Euler’s formula, says the following. If a connected graph G is 2-cell embedded into a closed surface with v vertices, edges and r regions, then v- e+ r = χ(s), where χ(s) is the Euler characteristic of s.
We’ll visit some of this history and then give a generalization of this formula that applies to any graph (connected or not), any surface (orientable or not) and any embedding (2-cell or not). One striking corollary is the converse of Euler’s formula itself: If an embedding of a graph G into a surface has the ”right” number of regions for a 2-cell embedding, then it IS a 2-cell embedding.
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ID de reunión: 675 648 7475
Código de acceso: V2hgZi!!
