Author(s)

Yongqiang Zhao¹, Zhiming Fang^2,3, Yonggang Cui¹, Guoyan Ye¹, Zhijun Cao¹

¹School of Science, Shijiazhuang University, Shijiazhuang, China.
²Zhejiang Jinyun High School, Lishui, China.
³School of Science, Hebei University of Technology, Tianjin, China.

It is hard to compute the competition number for a graph in general and characterizing a graph by its competition number has been one of important research problems in the study of competition graphs. Sano pointed out that it would be interesting to compute the competition numbers of some triangulations of a sphere as he got the exact value of the competition numbers of regular polyhedra. In this paper, we study the competition numbers of several kinds of triangulations of a sphere, and get the exact values of the competition numbers of a 24-hedron obtained from a hexahedron by adding a vertex in each face of the hexahedron and joining the vertex added in a face with the four vertices of the face, a class of dodecahedra constructed from a hexahedron by adding a diagonal in each face of the hexahedron, and a triangulation of a sphere with 3n (n≥2) vertices.

Competition Graph, Competition Number, Edge Clique Cover, Vertex Clique Cover, Triangulation of a Sphere

Zhao, Y. , Fang, Z. , Cui, Y. , Ye, G. and Cao, Z. (2017) Competition Numbers of Several Kinds of Triangulations of a Sphere. Open Journal of Discrete Mathematics, 7, 54-64. doi: 10.4236/ojdm.2017.72006.