The crossing number of the hexagonal graph H_{3,n}
Yuanqiu Huang, Zhangdong Ouyang, Jing Wang · Discussiones Mathematicae Graph Theory · 2018
In [C. Thomassen, Tilings of the torus and the Klein bottle and vertextransitive graphs on a fixed surface, Trans. Amer. Math. Soc. 323 (1991) 605-635], Thomassen described completely all (except finitely many) regular tilings of the torus S 1 and the Klein bottle N 2 into (3,6)-tilings, (4,4)-tilings and (6,3)-tilings. Many authors made great efforts to investigate the crossing number (in the plane) of the Cartesian product of an m-cycle and an n-cycle, which is a special (4,4)-tiling. For other tilings, there are quite rare results concerning on their crossing numbers. This motivates us in the paper to determine the crossing number of a hexagonal graph H 3,n , which is a special kind of (3,6)-tilings.