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Publication
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| Title of Article |
RELAXED DP-COLORING AND ANOTHER
GENERALIZATION OF DP-COLORING ON PLANAR
GRAPHS WITHOUT 4-CYCLES AND 7-CYCLES |
| Date of Acceptance |
23 April 2021 |
| Journal |
| Title of Journal |
Discussiones Mathematicae Graph Theory |
| Standard |
ISI |
| Institute of Journal |
University of Zielona Góra ul. Licealna 9 65-417 Zielona Góra, Poland |
| ISBN/ISSN |
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| Volume |
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| Issue |
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| Month |
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| Year of Publication |
2021 |
| Page |
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| Abstract |
DP-coloring is generalized via relaxed coloring and variable degeneracy
in [P. Sittitrai and K. Nakprasit, Sufficient 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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| Keyword |
relaxed DP-colorings, variable degeneracy, planar graphs, discharging |
| Author |
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| Reviewing Status |
มีผู้ประเมินอิสระ |
| Status |
ได้รับการตอบรับให้ตีพิมพ์ |
| Level of Publication |
นานาชาติ |
| citation |
false |
| Part of thesis |
true |
| Attach file |
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| Citation |
0
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Journal Publication
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