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A Generalization of Some Results on List Coloring and DP-Coloring

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Abstract

Let G be a graph and let \(f_i, i \in \{1,\ldots ,s\},\) be a function from V(G) to the set of nonnegative integers. In Sittitrai and Nakprasit (Analogue of DP-coloring on variable degeneracy and its applications, 2020), the concept of DP-F-coloring, a generalization of DP-coloring and variable degeneracy, was introduced. We use DP-F-coloring to define DPG-[k, t]-colorable graphs and modify the proofs in Liu et al. (Graphs Combin 35(3), 695–705, 2019), Sittitrai and Nakprasit (Bull Malays Math Sci Soc, 2019, https://doi.org/10.1007/s40840-019-00800-1), Thomassen (J Combin Theory Ser B 62, 180–181, 1994) to obtain more results on list coloring, DP-coloring, list-forested coloring, and variable degeneracy.

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Acknowledgements

We would like to thank Tao Wang for pointing out a few gaps of proofs and giving valuable suggestions for earlier versions of manuscript. We would like to thank the reviewer for the thorough comments that improves our presentation. Kittikorn Nakprasit is supported by the Commission on Higher Education and the Thailand Research Fund under Grant RSA6180049.

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  1. Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, 40002, Thailand

    Keaitsuda Maneeruk Nakprasit & Kittikorn Nakprasit

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  1. Keaitsuda Maneeruk Nakprasit
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  2. Kittikorn Nakprasit
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Correspondence to Kittikorn Nakprasit.

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Nakprasit, K.M., Nakprasit, K. A Generalization of Some Results on List Coloring and DP-Coloring. Graphs and Combinatorics 36, 1189–1201 (2020). https://doi.org/10.1007/s00373-020-02177-6

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  • DOI: https://doi.org/10.1007/s00373-020-02177-6

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