Describing the neighborhoods of 5-vertices in 3-polytopes with minimum degree 5 and no vertices of degree from 6 to 8☆

Add time:08/12/2019    Source:sciencedirect.com

In 1940, Lebesgue proved that every 3-polytope with minimum degree 5 contains a 5-vertex for which the set of degrees of its neighbors is majorized by one of the following sequences: (6,6,7,7,7),(6,6,6,7,9),(6,6,6,6,11),(5,6,7,7,8),(5,6,6,7,12),(5,6,6,8,10),(5,6,6,6,17),(5,5,7,7,13),(5,5,7,8,10),(5,5,6,7,27),(5,5,6,6,∞),(5,5,6,8,15),(5,5,6,9,11),(5,5,5,7,41),(5,5,5,8,23),(5,5,5,9,17),(5,5,5,10,14),(5,5,5,11,13).

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