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arXiv · 1807.00815

Analogue of DP-coloring on variable degeneracy and its applications on list vertex-arboricity and DP-coloring

Pongpat Sittitrai·Kittikorn Nakprasit
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Abstract

In \cite{listnoC3adjC4}), Borodin and Ivanova proved that every planar graph without $4$-cycles adjacent to $3$-cycle is list vertex-$2$-aborable. In fact, they proved a more general result. Inspired by these results and DP-coloring which becomes a widely studied topic, we introduce a generalization on variable degeneracy including list vertex arboricity. We use this notion to extend a general result by Borodin and Ivanova. Not only that this theorem implies results about planar graphs without $4$-cycles adjacent to $3$-cycle by Borodin and Ivanova, it implies many other results including a result by Kim and Yu \cite{KimY} that every planar graph without $4$-cycles adjacent to $3$-cycle is DP-$4$-colorable.

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Pongpat Sittitrai, Kittikorn Nakprasit. 2018-07-02. Analogue of DP-coloring on variable degeneracy and its applications on list vertex-arboricity and DP-coloring. https://arxiv.org/abs/1807.00815

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