DMS Combinatorics Seminar

Speaker: Songling Shan (Auburn  University)

Title: Linear arboricity of graphs with large minimum degree

Abstract: In 1980, Akiyama, Exoo, and Harary conjectured that any graph $G$ can be decomposed into at most $\lceil(\Delta(G)+1)/2\rceil$ linear forests. We confirm the conjecture for sufficiently large graphs with large minimum degree. Precisely, we show that for any given $0<\varepsilon <1$, there exists  $n_0 \in \mathbb{N}$ for which the following statement holds: If $G$  is a graph on $n\ge n_0$ vertices of  minimum degree at least $(1+\varepsilon)n/2$, then $G$ can be decomposed into at most $\lceil(\Delta(G)+1)/2\rceil$ linear forests.  

This is joint work with Yuping Gao.