Describing Neighborhoods of 5-Vertices in 3-Polytopes with Minimum Degree 5 and Without Vertices of Degrees from 7 to 11 - Borodin Oleg V. (Discussiones Mathematicae Graph Theory, 2018)
In 1940, Lebesgue proved that every 3-polytope contains a 5-vertex for which the set of degrees of its neighbors is majorized by one of the following sequences: