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Cycle-Compelling Colorings of Graphs

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Combinatorics, Graph Theory and Computing (SEICCGTC 2021)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 448))

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Abstract

We define a cycle-compelling coloring of a graph as a proper coloring of the vertices such that every subgraph induced by one vertex of each color contains a cycle. The cycle-compelling number is defined to be the minimum k such that some k-coloring is cycle-compelling. We provide some general bounds and algorithmic results on this and related parameters. We also investigate the value in specific graph families including cubic graphs, disjoint union of cliques, and outerplanar graphs.

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References

  1. Bachstein, A., Goddard, W., Henning, M.A., Xue, J.: Compelling colorings: A generalization of the dominator chromatic number, submitted. Appl. Math. Comput. 428, 127193 (2022)

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Acknowledgements

Thanks to the audience members at the talk for their questions that, in particular, suggested considering the guaranteed version.

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Authors and Affiliations

  1. School of Mathematical and Statistical Sciences, Clemson University, Clemson, USA

    Anna Bachstein, Wayne Goddard & John Xue

Authors
  1. Anna Bachstein
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  2. Wayne Goddard
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  3. John Xue
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Corresponding author

Correspondence to Wayne Goddard .

Editor information

Editors and Affiliations

  1. Mathematical Sciences, Florida Atlantic University, Boca Raton, FL, USA

    Frederick Hoffman

  2. Mathematics, Kennesaw State University, Kennesaw, GA, USA

    Sarah Holliday

  3. Mathematics, Florida Atlantic University, Boca Raton, FL, USA

    Zvi Rosen

  4. Computer Science and Engineering, University of North Texas, Denton, TX, USA

    Farhad Shahrokhi

  5. Whiting School of Engineering, Johns Hopkins University, Baltimore, MD, USA

    John Wierman

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© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG

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Bachstein, A., Goddard, W., Xue, J. (2024). Cycle-Compelling Colorings of Graphs. In: Hoffman, F., Holliday, S., Rosen, Z., Shahrokhi, F., Wierman, J. (eds) Combinatorics, Graph Theory and Computing. SEICCGTC 2021. Springer Proceedings in Mathematics & Statistics, vol 448. Springer, Cham. https://doi.org/10.1007/978-3-031-52969-6_19

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