Relaxed DP-Coloring and another Generalization of DP-Coloring on Planar Graphs without 4-Cycles and 7-Cycles
DP-coloring is generalized via relaxed coloring and variable degeneracy in [P. Sittitrai and K. Nakprasit, , Graphs Combin. 35 (2019) 837–845], [K.M. Nakprasit and K. Nakprasit, , Graphs Combin. 36 (2020) 1189–1201] and [P. Sittitrai and K. Nakprasit, , Discuss. Math. Graph Theory]. In this work, we...
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Published in | Discussiones Mathematicae. Graph Theory Vol. 43; no. 1; pp. 287 - 297 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
Sciendo
01.02.2023
University of Zielona Góra |
Subjects | |
Online Access | Get full text |
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Summary: | DP-coloring is generalized via relaxed coloring and variable degeneracy in [P. Sittitrai and K. Nakprasit,
, Graphs Combin. 35 (2019) 837–845], [K.M. Nakprasit and K. Nakprasit,
, Graphs Combin. 36 (2020) 1189–1201] and [P. Sittitrai and K. Nakprasit,
, 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
[
, 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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ISSN: | 1234-3099 2083-5892 |
DOI: | 10.7151/dmgt.2405 |