Relaxed DP-Coloring and another Generalization of DP-Coloring on Planar Graphs without 4-Cycles and 7-Cycles

IF 0.5 4区数学 Q3 MATHEMATICS

Discussiones Mathematicae Graph Theory Pub Date : 2022-11-25 DOI:10.7151/dmgt.2405

Sarawute Sribunhung, K. Nakprasit, Kittikorn Nakprasit, Pongpat Sittitrai

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引用次数: 3

Abstract

Abstract DP-coloring is generalized via relaxed coloring and variable degeneracy in [P. Sittitrai and K. Nakprasit, Su cient conditions on planar graphs to have a relaxed DP-3-coloring, Graphs Combin. 35 (2019) 837–845], [K.M. Nakprasit and K. Nakprasit, A generalization of some results on list coloring and DP-coloring, Graphs Combin. 36 (2020) 1189–1201] and [P. Sittitrai and K. Nakprasit, An analogue of DP-coloring for variable degeneracy and its applications, Discuss. Math. Graph Theory]. In this work, we introduce another concept that includes two previous generalizations. We demonstrate its application on planar graphs without 4-cycles and 7-cycles. One implication is that the vertex set of every planar graph without 4-cycles and 7-cycles can be partitioned into three sets in which each of them induces a linear forest and one of them is an independent set. Additionally, we show that every planar graph without 4-cycles and 7-cycles is DP-(1, 1, 1)-colorable. This generalizes a result of Lih et al. [A note on list improper coloring planar graphs, Appl. Math. Lett. 14 (2001) 269–273] that every planar graph without 4-cycles and 7-cycles is (3, 1)*-choosable.

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无4环和7环平面图上的松弛DP染色和DP染色的另一个推广

摘要DP着色通过松弛着色和变简并性在[P.Sittitrai和K.Nakprasit，平面图上具有松弛DP-3-着色的充分条件，graphs Combin.35（2019）837–845]，[K.M.Nakprasat和K.Nacprasit，列表着色和DP着色的一些结果的推广，GraphsCombin.36（2020）1189–1201]和[P.Sittirai和K。Nakprasit，变简并性DP染色的一个类似物及其应用，讨论。数学图论]。在这项工作中，我们引入了另一个概念，其中包括前面的两个概括。我们证明了它在没有4环和7环的平面图上的应用。一个含义是，每个没有4环和7环的平面图的顶点集可以划分为三个集，其中每个集都诱导一个线性森林，其中一个是独立集。此外，我们还证明了每一个没有4环和7环的平面图都是DP-（1，1，1）-可着色的。这推广了Lih等人的一个结果。[关于列表不适当着色平面图的注记，Appl.Math.Lett.14（2001）269–273]认为，每个没有4环和7环的平面图都是（3，1）*可选择的。

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来源期刊

Discussiones Mathematicae Graph Theory MATHEMATICS-

CiteScore

2.20

自引率

0.00%

发文量

审稿时长

53 weeks

期刊介绍： The Discussiones Mathematicae Graph Theory publishes high-quality refereed original papers. Occasionally, very authoritative expository survey articles and notes of exceptional value can be published. The journal is mainly devoted to the following topics in Graph Theory: colourings, partitions (general colourings), hereditary properties, independence and domination, structures in graphs (sets, paths, cycles, etc.), local properties, products of graphs as well as graph algorithms related to these topics.