The Planar Ramsey Numbers PR (K<sub>4</sub>-e, K<sub>l</sub>)

• 作者: Rui Zhang Yali Wu Yongqi Sun Yuansheng Yang
• 来源期刊: 美国计算数学期刊(英文)
• 学科: 数学
• 关键词: PLANAR GRAPH RAMSEY Number Forbidden SUBGRAPH
• 年，卷（期）: mgjssxqkyw_2013,（3）
• 页码范围: 52-55
• 页数: 4页
• 分类号: O1

摘要

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).