Low 5-stars in normal plane maps with minimum degree 5.

In 1996, Jendrol’ and Madaras constructed a plane triangulation with minimum degree 5 in which the minimum vertex degree h ( S 5 ) of 5-stars is arbitrarily large. This construction has minor ( 5 , 5 , 5 , 5 ) -stars, that is 5-vertices with four 5-neighbors. It has been open if forbidding minor ( 5 , 5 , 5 , 5 ) -stars makes h ( S 5 ) finite. We prove that every normal plane map with minimum degree 5 and no minor ( 5 , 5 , 5 , 5 ) -stars satisfies h ( S 5 ) ≤ 13 and construct such a map with h ( S 5 ) = 12 . [ABSTRACT FROM AUTHOR]