Kim, S.R., Lee, J.Y., Park, B. and Sano, Y. (2012) The Competition Number of a Graph and the Dimension of Its Hole Space. Applied Mathematics Letters, 25, 638-642.
https://doi.org/10.1016/j.aml.2011.10.003

has been cited by the following article:

• TITLE: Competition Numbers of Several Kinds of Triangulations of a Sphere

  AUTHORS: Yongqiang Zhao, Zhiming Fang, Yonggang Cui, Guoyan Ye, Zhijun Cao

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

  JOURNAL NAME: Open Journal of Discrete Mathematics, Vol.7 No.2, April 19, 2017

  ABSTRACT: 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.