Low stars in normal plane maps with minimum degree 4 and no adjacent 4-vertices

摘要

We consider normal plane maps M-4* with minimum degree at least 4 and no adjacent 4-vertices. The height of a star is the maximum degree of its vertices. By h(S-k) and h(Si(cm)) with 1 <= k <= 4 we denote the minimum height of arbitrary k-stars and k-stars centered at vertices of degree at most 5, respectively, in a given M-4*.