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Graphs and Combinatorics

, Volume 35, Issue 6, pp 1659–1671 | Cite as

Complete Graph-Tree Planar Ramsey Numbers

  • Yaojun Chen
  • Xiaolan HuEmail author
Original Paper
  • 39 Downloads

Abstract

For two given graphs \(G_1\) and \(G_2\), the planar Ramsey number \(PR( G_1,G_2)\) is the smallest integer N such that every planar graph G on N vertices either contains a copy of \(G_1\) or its complement contains a copy of \(G_2\). In this paper, we determine all planar Ramsey numbers for the complete graphs versus trees.

Keywords

Planar Ramsey numbers Complete graphs Trees 

Notes

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Copyright information

© Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsNanjing UniversityNanjingPeople’s Republic of China
  2. 2.School of Mathematics and StatisticsCentral China Normal UniversityWuhanPeople’s Republic of China

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