Total Colorings of Planar Graphs with Small Maximum Degree
نویسندگان
چکیده
Let G be a planar graph of maximum degree ∆ and girth g, and there is an integer t(> g) such that G has no cycles of length from g+1 to t. Then the total chromatic number of G is ∆+1 if (∆,g, t) ∈ {(5,4,6),(4,4,17)}; or ∆ = 3 and (g, t) ∈ {(5,13),(6,11),(7,11), (8,10),(9,10)}, where each vertex is incident with at most one g-cycle. 2010 Mathematics Subject Classification: 05C15
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