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Gallai—Ramsey Number for the Union of Stars

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Abstract

Given a graph G and a positive integer k, define the Gallai—Ramsey number to be the minimum number of vertices n such that any k-edge coloring of Kn contains either a rainbow (all different colored) triangle or a monochromatic copy of G. In this paper, we obtain exact values of the Gallai—Ramsey numbers for the union of two stars in many cases and bounds in other cases. This work represents the first class of disconnected graphs to be considered as the desired monochromatic subgraph.

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Acknowledgements

We would like to thank the anonymous referees for a number of helpful comments and suggestions.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Qinghai Normal University, Xining, 810008, P. R. China

    Ya Ping Mao

  2. College of Science, China Jiliang University, Hangzhou, 310018, P. R. China

    Zhao Wang

  3. Department of Mathematics, Clayton State University, Morrow, GA, 30260, USA

    Colton Magnant

  4. Technische Universität Bergakademie Freiberg, Institut für Diskrete Mathematik und Algebra, 09596, Freiberg, Germany

    Ingo Schiermeyer

Authors
  1. Ya Ping Mao
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  2. Zhao Wang
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  3. Colton Magnant
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  4. Ingo Schiermeyer
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Corresponding author

Correspondence to Zhao Wang.

Additional information

Supported by the National Science Foundation of China (Grant Nos. 12061059 and 61763041)

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Mao, Y.P., Wang, Z., Magnant, C. et al. Gallai—Ramsey Number for the Union of Stars. Acta. Math. Sin.-English Ser. 38, 1317–1332 (2022). https://doi.org/10.1007/s10114-022-0467-1

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  • DOI: https://doi.org/10.1007/s10114-022-0467-1

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