Planar Ramsey Numbers of Four Cycles Versus Wheels
Chen Yaojun, Miao Zhengke, Zhou Guofei

TL;DR
This paper determines the exact planar Ramsey numbers for pairs of graphs involving a 4-cycle and wheels, by analyzing structural properties of $C_4$-free planar graphs.
Contribution
It characterizes structural properties of $C_4$-free planar graphs and computes all $PR(C_4, W_n)$ for $n \u2265 3$, advancing understanding of planar Ramsey numbers.
Findings
Determined all $PR(C_4, W_n)$ for $n \u2265 3$.
Characterized structural properties of $C_4$-free planar graphs.
Abstract
For two given graphs and the planar Ramsey number is the smallest integer such that every planar graph on vertices either contains a copy of , or its complement contains a copy of . In this paper, we first characterize some structural properties of -free planar graphs, and then we determine all planar Ramsey numbers , for .
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Graph Theory Research · Graph Labeling and Dimension Problems
