The list linear arboricity of graphs

초록

A linear forest is a forest in which every connected component is a path. The linear arboricity of a graph G is the minimum number of linear forests of G covering all edges. In 1980, Akiyama, Exoo, and Harary proposed a conjecture, known as the Linear Arboricity Conjecture (LAC), stating that every Delta-regular graph G has linear arboricity left ceiling Delta + 1 2 right ceiling . In 1988, Alon proved that the LAC holds asymptotically. In 1999, the list version of the LAC was raised by An and Wu, which is called the List Linear Arboricity Conjecture. In this article, we prove that the List Linear Arboricity Conjecture holds asymptotically.

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