10 problems

Let $G$ be an undirected graph with maximum degree $\Delta$, let $la(G)$ be its linear arboricity, and let $lla(G)$ be its list linear arboricity. List Linear Arboricity Conjecture…

Odd-degree planar edge-partition conjecture. The edges of $G$ can be partitioned into $\tfrac{\Delta-1}{2}$ linear forests and one matching.

Planar Linear Arboricity Conjecture. For every planar graph $G$ of maximum degree $\Delta\ge 5$,

Directed Linear Arboricity Conjecture. For every directed graph $D$,

Linear Arboricity Conjecture. For every simple graph $G$,

Akiyama's linear arboricity conjecture. For every graph $G$ of maximum degree $\Delta$,

Let $\Sigma$ be a simple signed graph, let $\Delta(\Sigma)$ be its maximum degree, and let $\chi'_R(\Sigma)$ be the minimum number of colors in a completely reversible zero-free pr…

Strong Ando conjecture. Every cubic graph admits a bisection such that the two induced subgraphs are isomorphic linear forests.

Wormald's conjecture. There exists a linear partition of $G$ into two isomorphic linear forests.

Planar degree-four linear arboricity complexity conjecture. It is NP-complete to determine whether