Geodesic
A note on total colorings of planar graphs without 4-cycles
Discussiones Mathematicae. Graph Theory, Tome 24 (2004) no. 1, pp. 125-135

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Let G be a 2-connected planar graph with maximum degree Δ such that G has no cycle of length from 4 to k, where k ≥ 4. Then the total chromatic number of G is Δ +1 if (Δ,k) ∈ (7,4),(6,5),(5,7),(4,14).
Keywords: total coloring, planar graph, list coloring, girth 
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     title = {A note on total colorings of planar graphs without 4-cycles},
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Wang, Ping; Wu, Jian-Liang. A note on total colorings of planar graphs without 4-cycles. Discussiones Mathematicae. Graph Theory, Tome 24 (2004) no. 1, pp. 125-135. http://geodesic.mathdoc.fr/item/DMGT_2004_24_1_a10/