A Weak DP-Partitioning of Planar Graphs without 4-Cycles and 6-Cycles

In this paper, we introduce a weak DP-partitioning which combines the concepts of DP-coloring and vertex-partition. Let G be a planar graph without 4- and 6-cycles. We show that G is weakly DP- ( F 2 , F ) -colorable. The result implies that G has a partition of the vertex set into two sets, where o...

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Bibliographic Details
Published inBulletin of the Malaysian Mathematical Sciences Society Vol. 46; no. 4
Main Authors Sittitrai, Pongpat, Nakprasit, Keaitsuda Maneeruk, Nakprasit, Kittikorn
Format Journal Article
LanguageEnglish
Published Singapore Springer Nature Singapore 01.07.2023
Springer Nature B.V
Subjects
Applications of Mathematics
Mathematics
Mathematics and Statistics
Partitioning
Partitions (mathematics)
Vertex sets
05C10
Discharging method
Forest partition
Planar graphs
DP-coloring
05C15
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Summary:In this paper, we introduce a weak DP-partitioning which combines the concepts of DP-coloring and vertex-partition. Let G be a planar graph without 4- and 6-cycles. We show that G is weakly DP- ( F 2 , F ) -colorable. The result implies that G has a partition of the vertex set into two sets, where one set induces a forest, and the other induces a linear forest as shown by Huang et al. We also prove that G is weakly DP- ( F 2 , F 0 , F 0 ) -colorable which improves the result by Fang and Wang that G is weakly DP- ( F 2 , F 2 , F 0 ) -colorable.
ISSN:0126-6705
2180-4206
DOI:10.1007/s40840-023-01528-9