I. Gorgol, “Planar Ramsey Numbers,” Discussiones Mathematicae Graph Theory, Vol. 25, No. 1-2, 2005, pp. 45-50. doi:10.7151/dmgt.1258

has been cited by the following article:

• TITLE: The Planar Ramsey Numbers PR (K4-e, Kl)

  AUTHORS: Yongqi Sun, Yali Wu, Rui Zhang, Yuansheng Yang

  KEYWORDS: Planar Graph; Ramsey Number; Forbidden Subgraph

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.3 No.3B, October 25, 2013

  ABSTRACT: The planar Ramsey number PR (H1, H2) is the smallest integer n such that any planar graph on n vertices contains a copy of H1 or its complement contains a copy of H2. It is known that the Ramsey number R(K4 -e, K6) = 21, and the planar Ramsey numbers PR(K4 - e, Kl) for l ≤ 5 are known. In this paper, we give the lower bounds on PR (K4 ? e, Kl) and determine the exact value of PR (K4 - e, K6).