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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Published in | Bulletin of the Malaysian Mathematical Sciences Society Vol. 46; no. 4 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Singapore
Springer Nature Singapore
01.07.2023
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
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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. |
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ISSN: | 0126-6705 2180-4206 |
DOI: | 10.1007/s40840-023-01528-9 |