The Crossing Number of Hexagonal Graph H3,n in the Projective Plane

Discussiones Mathematicae Graph Theory

卷:42

Wang Jing¹  Huang Yuanqiu²  Cai Junliang³  Lv Shengxiang⁴ 

[1] College of Mathematics and Computer Science, Changsha University, Changsha410022, China;

[2] College of Mathematics and Computer Science, Hunan Normal University, Changsha410081, China;

[3] School of Mathematical Sciences, Beijing Normal University, Beijing100875, China;

[4] School of Mathematics and Statistics, Hunan University of Finance and Economics, ChangSha, 410205, China;

关键词: projective plane;    crossing number;    hexagonal graph;    drawing;    05c10;    05c62;   

DOI  :  10.7151/dmgt.2251

来源: DOAJ

【 摘 要 】

Thomassen described all (except finitely many) regular tilings of the torus S1 and the Klein bottle N2 into (3,6)-tilings, (4,4)-tilings and (6,3)-tilings. Many researchers made great e orts to investigate the crossing number of the Cartesian product of an m-cycle and an n-cycle, which is a special kind of (4,4)-tilings, either in the plane or in the projective plane. In this paper we study the crossing number of the hexagonal graph H3,n (n ≥ 2), which is a special kind of (3,6)-tilings, in the projective plane, and prove that crN1(H3,n)={0,n=2,n-1,n≥3.cr{N_1}\left( {{H_{3,n}}} \right) = \left\{ {\matrix{{0,} \hfill & {n = 2,} \hfill\cr {n - 1,} \hfill & {n \ge 3.} \hfill\cr} } \right.

【 授权许可】

Unknown