We prove that the linear arboricity of every 5‐regular graph is 3. That is, the edges of any 5‐regular graph are covered by three linear forests. We also determine the linear arboricity of 6‐regular graphs and 8‐regular graphs. These results improve the known upper bounds for the linear arboricity of graphs with given maximum degree.
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Enomoto et al. (1984) studied this question.
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