Lee, J.Y., Kim, S.-R., Kim, S.-J. and Sano, Y. (2011) Graphs Having Many Holes but with Small Competition Numbers. Applied Mathematics Letters, 24, 1331-1335.
https://doi.org/10.1016/j.aml.2011.03.003

has been cited by the following article:

• TITLE: Competition Numbers of a Kind of Pseudo-Halin Graphs

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

  KEYWORDS: Competition Graph, Competition Number, Halin Graph, Generalized Halin Graph, Pseudo-Halin Graph

  JOURNAL NAME: Open Journal of Discrete Mathematics, Vol.7 No.1, December 30, 2016

  ABSTRACT: For any graphG,Gtogether with sufficiently many isolated vertices is the competition graph of some acyclic digraph. The competition numberk(G)of a graphGis defined to be the smallest number of such isolated vertices. In general, it is hard to compute the competition numberk(G)for a graphGand chara-cterizing a graph by its competition number has been one of important research problems in the study of competition graphs. A 2-connected planar graphGwith minimum degree at least 3 is a pseudo-Halin graph if deleting the edges on the boundary of a single facef0yields a tree. It is a Halin graph if the vertices off0all have degree 3 inG. In this paper, we compute the competition numbers of a kind of pseudo-Halin graphs.