Complete minimal spheres and projective planes inRnwith simple ends

Minimal graphs of a torus, a projective

Minimal graphs of a torus, a projective plane and spheres and some properties of minimal graphs of homotopy classes

✍ Alexander V. Ivashchenko; Yeong-Nan Yeh 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 397 KB

## Contractible transformations of graphs consist of contractible gluing and deleting of vertices and edges of graphs. They partition all graphs into the family of homotopy classes. Contractible transformations do not change the Euler characteristic and the homology groups of graphs. In this paper