5-stars of low weight in normal plane maps with minimum degree 5
Oleg Veniaminovich Borodin, Anna O. Ivanova, Tommy R. Jensen · Discussiones Mathematicae Graph Theory · 2014
It is known that there are normal plane maps M 5 with minimum degree 5 such that the minimum degree-sum w(S 5 ) of 5-stars at 5-vertices is arbitrarily large. In 1940, Lebesgue showed that if an M 5 has no 4-stars of cyclic type (5, 6, 6, 5) centered at 5-vertices, then w(S 5 ) 68. We improve this bound of 68 to 55 and give a construction of a (5, 6, 6, 5)-free M 5 with w(S 5 ) = 48.