Borut Lužar: On the linear arboricity of graphs

The linear arboricity $la(G)$ of a graph $G$ is the minimum number of linear forests that partition the edges of $G$. In 1984, Akiyama, Exoo, and Harary posed a conjecture that for any simple graph $G$ holds
$$
   \lceil \frac{\Delta(G)}{2} \rceil \le \la{G} \le \lceil \frac{\Delta(G) + 1}{2} \rceil.
$$
The conjecture has been proved for several classes of graphs. At the seminar we will present a short proof for cubic graphs and present some recent results related to planar graphs.