(Δ+1)(Δ+1)-total-colorability of plane graphs of maximum degree Δ⩾6Δ⩾6 with neither chordal 5-cycle nor chordal 6-cycle

In this paper, we prove that a plane graph of maximum degree Δ⩾6Δ⩾6 is (Δ+1)(Δ+1)-totally-colorable if it contains neither chordal 5-cycle nor chordal 6-cycle. This further extends the known class of plane graphs of maximum degree Δ   in which every graph is (Δ+1)(Δ+1)-totally-colorable.

► We study total coloring of plane graphs.
► Concern (Δ+1)(Δ+1)-total-colorability of plane graphs.
► Extend the known class of plane graphs which are (Δ+1)(Δ+1)-totally-colorable.