Planar Graphs without Cycles of Length 3, 4, and 6 are (3, 3)-Colorable

Pongpat Sittitrai, Wannapol Pimpasalee and Anwar Saleh Alwardi

International Journal of Mathematics and Mathematical Sciences, 2024, vol. 2024, 1-4

Abstract: For non-negative integers d1 and d2, if V1 and V2 are two partitions of a graph G’s vertex set VG, such that V1 and V2 induce two subgraphs of G, called GV1 with maximum degree at most d1 and GV2 with maximum degree at most d2, respectively, then the graph G is said to be improper d1,d2-colorable, as well as d1,d2-colorable. A class of planar graphs without C3,C4, and C6 is denoted by C. In 2019, Dross and Ochem proved that G is 0,6-colorable, for each graph G in C. Given that d1+d2≥6, this inspires us to investigate whether G is d1,d2-colorable, for each graph G in C. In this paper, we provide a partial solution by showing that G is (3, 3)-colorable, for each graph G in C.

Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/ijmms/2024/7884281.pdf (application/pdf)
http://downloads.hindawi.com/journals/ijmms/2024/7884281.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:7884281

DOI: 10.1155/2024/7884281

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().