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

详细信息    查看全文

• 作者：O.V. Borodin^a ; ^{brdnoleg@math.nsc.ru} ; A.O. Ivanova^b ; ^{shmgnanna@mail.ru}
• 关键词：Normal plane map ; Plane graph ; 3-polytope ; Structural property ; Star ; Height
• 刊名：Discrete Mathematics
• 出版年：2017
• 出版时间：6 February 2017
• 年：2017
• 卷：340
• 期：2
• 页码：18-22
• 全文大小：433 K
• 卷排序：340

文摘

In 1996, Jendrol’ and Madaras constructed a plane triangulation with minimum degree 5 in which the minimum vertex degree h(S5)h(S5) of 5-stars is arbitrarily large. This construction has minor (5,5,5,5)(5,5,5,5)-stars, that is 5-vertices with four 5-neighbors. It has been open if forbidding minor (5,5,5,5)(5,5,5,5)-stars makes h(S5)h(S5) finite.We prove that every normal plane map with minimum degree 5 and no minor (5,5,5,5)(5,5,5,5)-stars satisfies h(S5)≤13h(S5)≤13 and construct such a map with h(S5)=12h(S5)=12.