  In this expository 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.
