Competition Numbers of Several Kinds of Triangulations of a Sphere

• 作者: Guoyan Ye Yonggang Cui Yongqiang Zhao Zhijun Cao Zhiming Fang
• 来源期刊: 离散数学期刊(英文)
• 学科: 数学
• 关键词: COMPETITION Graph COMPETITION Number Edge CLIQUE COVER Vertex CLIQUE COVER TRIANGULATION of a SPHERE
• 年，卷（期）: 2017,（2）
• 页码范围: 54-64
• 页数: 11页
• 分类号: O1

摘要

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.