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The list linear arboricity of graphs
Author(s) -
Kim Ringi,
Postle Luke
Publication year - 2021
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.22685
Subject(s) - arboricity , mathematics , combinatorics , conjecture , degeneracy (biology) , dense graph , graph , discrete mathematics , pathwidth , planar graph , line graph , biology , bioinformatics
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 Δ ‐regular graph G has linear arboricity ⌈ Δ + 1 2 ⌉ . 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.