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.