Article citationsMore>>

Roussel, N. (2011) Local Condition for Planar Graphs of Maximum Degree 6 to Be Total 8-Colorable. Taiwanese Journal of Mathematics, 15, 87-99.
https://doi.org/10.11650/twjm/1500406163

has been cited by the following article:

• TITLE: On the (Δ + 2)-Total-Colorability of Planar Graphs with 7-Cycles Containing at Most Two Chords

  AUTHORS: Jian Chang, Jingru Liu, Fan Zhang

  KEYWORDS: Planar Graph, 7-Cycle, 8-Totally-Colorable, Maximum Degree

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.12 No.7, July 31, 2024

  ABSTRACT: The Total Coloring Conjecture (TCC) proposes that every simple graph G is (Δ + 2)-totally-colorable, where Δ is the maximum degree of G. For planar graph, TCC is open only in case Δ = 6. In this paper, we prove that TCC holds for planar graph with Δ = 6 and every 7-cycle contains at most two chords.