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All Complete Graph-Wheel Planar Ramsey Numbers

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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 for any planar graph \(G\) of order \(N\), either \(G\) contains \(G_1\) or the complement of \(G\) contains \(G_2\). Let \(K_m\) denote a complete graph of order \(m\) and \(W_n\) a wheel of order \(n+1\). In this paper, we determine all planar Ramsey numbers \(PR(K_m,W_n)\).

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Acknowledgments

This research was supported by NSFC under Grant Numbers 11071115, 11371193 and 11101207, and in part by the Priority Academic Program Development of Jiangsu Higher Education Institutions.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University, Nanjing, 210093, China

    Yanbo Zhang, Guofei Zhou & Yaojun Chen

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  1. Yanbo Zhang
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  2. Guofei Zhou
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  3. Yaojun Chen
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Correspondence to Yaojun Chen.

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Zhang, Y., Zhou, G. & Chen, Y. All Complete Graph-Wheel Planar Ramsey Numbers. Graphs and Combinatorics 31, 2459–2465 (2015). https://doi.org/10.1007/s00373-014-1509-y

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  • DOI: https://doi.org/10.1007/s00373-014-1509-y

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