Quiz

because we have 3 vertices with odd degrees

Actually, there are 4: A, C, E, F, since A is connected to B, D, E, and F by two curves. Everything else is correct; there should be no more than 2 vertices with odd degrees. Guess.

P.S. A fellow traveler from St. Petersburg to Moscow once proposed this problem. It was like a bet: if you draw it before we arrive, I'll pay you $100; if not, you pay me. Hermit, was that you by any chance?:D I refused, of course...