Linear arboricity of robust expanders
Abstract
In 1980, Akiyama, Exoo, and Harary conjectured that any graph G can be decomposed into at most ((G)+1)/2 linear forests. We confirm the conjecture for robust expanders of linear minimum degree. As a consequence, the conjecture holds for dense quasirandom graphs of linear minimum degree as well as for large n-vertex graphs with minimum degree arbitrarily close to n/2 from above.
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