- Tytuł:
- An Analogue of DP-Coloring for Variable Degeneracy and its Applications
- Autorzy:
-
Sittitrai, Pongpat
Nakprasit, Kittikorn - Powiązania:
- https://bibliotekanauki.pl/articles/32361750.pdf
- Data publikacji:
- 2022-02-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
DP-colorings
arboricity colorings
planar graphs - Opis:
- A graph G is list vertex k-arborable if for every k-assignment L, one can choose f(v) ∈ L(v) for each vertex v so that vertices with the same color induce a forest. In [6], Borodin and Ivanova proved that every planar graph without 4-cycles adjacent to 3-cycles is list vertex 2-arborable. In fact, they proved a more general result in terms of variable degeneracy. Inspired by these results and DP-coloring which is a generalization of list coloring and has become a widely studied topic, we introduce a generalization on variable degeneracy including list vertex arboricity. We use this notion to extend a general result by Borodin and Ivanova. Not only this theorem implies results about planar graphs without 4-cycles adjacent to 3-cycle by Borodin and Ivanova, it also implies other results including a result by Kim and Yu [S.-J. Kim and X. Yu, Planar graphs without 4-cycles adjacent to triangles are DP-4-colorable, Graphs Combin. 35 (2019) 707–718] that every planar graph without 4-cycles adjacent to 3-cycles is DP-4-colorable.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2022, 42, 1; 89-99
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł