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Weak Dynamic Coloring of Planar Graphs

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Abstract

The k-weak-dynamic number of a graph G is the smallest number of colors we need to color the vertices of G in such a way that each vertex v of degree d(v) sees at least min\(\{k,d(v)\}\) colors on its neighborhood. We use reducible configurations and list coloring of graphs to prove that all planar graphs have 3-weak-dynamic number at most 6.

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Acknowledgements

The authors would like to thank the anonymous referee, whose suggestions greatly improved the exposition of this paper.

Funding

NSF grant CMMI-1727743. NSF grant REU-1659075.

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Authors and Affiliations

  1. Department of Mathematics, DeSales University, Center Valley, PA, USA

    Caroline Accurso

  2. School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY, USA

    Vitaliy Chernyshov & Paul Wenger

  3. Department of Mathematics, Boise State University, Boise, ID, USA

    Leaha Hand

  4. Department of Mathematics and Statistics, San Jose State University, San Jose, CA, USA

    Sogol Jahanbekam

Authors
  1. Caroline Accurso
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  2. Vitaliy Chernyshov
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  3. Leaha Hand
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  4. Sogol Jahanbekam
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  5. Paul Wenger
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Correspondence to Sogol Jahanbekam.

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S. Jahanbekam: Research supported in part by NSF grant CMMI-1727743. C. Accurso, V. Chernyshov, L. Hand, S. Jahanbekam: Research supported in part by NSF grant REU-1659075.

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Accurso, C., Chernyshov, V., Hand, L. et al. Weak Dynamic Coloring of Planar Graphs. Graphs and Combinatorics 40, 27 (2024). https://doi.org/10.1007/s00373-023-02748-3

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  • DOI: https://doi.org/10.1007/s00373-023-02748-3

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