Special embeddings of graphs into a three-dimensional space
T. A. Antonova, K. I. Oblakov · Moscow University Mathematics Bulletin · 2008
Embeddings of graphs into ℝ 3 such that the minimal possible number of points are placed on each line are considered. A theorem stating that for any embedding into ℝ 3 of a pair of circumferences with a nonzero linking number there exists a line crossing this set at not less than 4 points is proved. Using this theorem, it is proved that Petersen graphs are minimal 3-nonembeddable.