# Woodall, Douglas R.

## List Total Colouring Conjecture ★★

Author(s): Borodin; Kostochka; Woodall

\begin{conjecture} If $G$ is the total graph of a multigraph, then $\chi_\ell(G)=\chi(G)$. \end{conjecture}

Keywords: list coloring; Total coloring; total graphs

## Woodall's Conjecture ★★★

Author(s): Woodall

\begin{conjecture} If $G$ is a directed graph with smallest directed cut of size $k$, then $G$ has $k$ disjoint dijoins. \end{conjecture}