A Note on Linear Arboricity of Graphs with Nonnegative Characteristic
نویسندگان
چکیده
A map from E (G) to {1, 2, 3, ..., t} is called a t-linear coloring if (V (G), φ(α)) is a linear forest for 1 ≤ α ≤ t. The linear arboricity la (G) of a graph G defined by Harary [9] is the minimum number t for which G has a t-linear coloring. Let G be a graph embeddable in a surface of nonnegative characteristic. In this paper, we prove that if G contains no 4-cycles and intersecting triangles and ∆ (G) ≤ 5, then la(G) ≤ 3. AMS 2000 SUBJECT CLASSIFICATION: 05C15, 05C78.
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