Embeddings into the plane of graphs with vertices of degree 4

Details Embeddings into the plane of graphs with vertices of degree 4 Embeddings into the plane of graphs with vertices of degree 4

2010-08-29

arxiv.org/abs/1008.4940v1

Mathematics

Combinatorics

4 pages, 5 figures, in Russian

Scientific paper

In this pedagogical note we present a proof of the V.A. Vassiliev conjecture on the planarity of graphs with vertices of degree 4 and certain additional structure. Both statement and proof are accessible to high-school students familiar with basic notions of graph theory. The conjecture was first proved by V.O. Manturov (such a proof was one of the main results of his habilitation thesis). In this note the exposition is made clearer and some comments for beginners are added.

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