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A note on total colorings of planar graphs without 4-cycles. (English) Zbl 1056.05067
Summary: Let \(G\) be a 2-connected planar graph with maximum degree \(\Delta\) such that \(G\) has no cycle of length from 4 to \(k\), where \(k\geq 4\). Then the total chromatic number of \(G\) is \(\Delta+1\) if \((\Delta,k)\in\{(7,4),(6,5), (5,7), (4,14)\}\).

05C15 Coloring of graphs and hypergraphs
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