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K. Walker, “The Analog of Ramsey Numbers for Planar Graphs,” Bulletin of the London Mathematical Society, Vol. 1, No. 2, 1969, pp. 187-190. doi:10.1112/blms/1.2.187

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).