“…(1) Δ ≥ 3 and g ≥ 8, or Δ ≥ 4 and g ≥ 5, or Δ ≥ 5 and g ≥ 4 ([1]) (2) Δ ≥ 6 without intersecting 3-cycles ( [4]) (3) Δ ≥ 6 without 4-or 5-cycles ( [5]) (4) Δ ≥ 6 without 5-or 6-cycles with chords [6] (5) Δ ≥ 6 without 5-cycles ( [7]) or 6-cycles ( [8]) with two chords (6) Δ ≥ 6 without 7-cycles ( [9]) or 6-cycles ( [10]) with three chords (7) Δ ≥ 6 and any vertex is incident with at most three triangles ( [11]) (8) Δ ≥ 6 and without adjacent k-cycles, where 3 ≤ k ≤ 6…”
In this paper, by applying the discharging method, we show that if
G
is a planar graph with a maximum degree of
Δ
=
6
that does not contain any adjacent 8-cycles, then
G
is of class 1.
“…(1) Δ ≥ 3 and g ≥ 8, or Δ ≥ 4 and g ≥ 5, or Δ ≥ 5 and g ≥ 4 ([1]) (2) Δ ≥ 6 without intersecting 3-cycles ( [4]) (3) Δ ≥ 6 without 4-or 5-cycles ( [5]) (4) Δ ≥ 6 without 5-or 6-cycles with chords [6] (5) Δ ≥ 6 without 5-cycles ( [7]) or 6-cycles ( [8]) with two chords (6) Δ ≥ 6 without 7-cycles ( [9]) or 6-cycles ( [10]) with three chords (7) Δ ≥ 6 and any vertex is incident with at most three triangles ( [11]) (8) Δ ≥ 6 and without adjacent k-cycles, where 3 ≤ k ≤ 6…”
In this paper, by applying the discharging method, we show that if
G
is a planar graph with a maximum degree of
Δ
=
6
that does not contain any adjacent 8-cycles, then
G
is of class 1.
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