# Kostochka, Alexandr V.

## 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

## Acyclic list colouring of planar graphs. ★★★

Author(s): Borodin; Fon-Der-Flasss; Kostochka; Raspaud; Sopena

\begin{conjecture} Every planar graph is acyclically 5-choosable. \end{conjecture}

Keywords:

## The Borodin-Kostochka Conjecture ★★

\begin{conjecture} Every graph with maximum degree $\Delta \geq 9$ has chromatic number at most $\max\{\Delta-1, \omega\}$. \end{conjecture}

Keywords:

## Bounding the chromatic number of triangle-free graphs with fixed maximum degree ★★

\begin{conjecture} A triangle-free graph with maximum degree $\Delta$ has chromatic number at most $\ceil{\frac{\Delta}{2}}+2$. % Enter your conjecture in LaTeX % You may change "conjecture" to "question" or "problem" if you prefer. \end{conjecture}

Keywords: chromatic number; girth; maximum degree; triangle free