an:07192855
Zbl 1437.05077
Liu, Jie; Lv, Jian-Bo
Every planar graph without 4-cycles and 5-cycles is \((2, 6)\)-colorable
EN
Bull. Malays. Math. Sci. Soc. (2) 43, No. 3, 2493-2507 (2020).
00448620
2020
j
05C15 05C10 05C38
improper coloring; planar graph; discharging method
Summary: A graph is \((d_1,\ldots ,d_r)\)-colorable if the vertex set can be partitioned into \(r\) sets \(V_1,\ldots ,V_r\) where the maximum degree of the subgraph induced by \(V_i\) is at most \(d_i\) for each \(i\in \{1,\ldots ,r\}\). In this paper, we prove that every planar graph without 4-cycles and 5-cycles is \((2, 6)\)-colorable, which improves the result of \textit{P. Sittitrai} and \textit{K. Nakprasit} [Discrete Math. 341, No. 8, 2142--2150 (2018; Zbl 1388.05072)], who proved that every planar graph without 4-cycles and 5-cycles is \((2, 9)\)-colorable.
Zbl 1388.05072