# Kostochka, Alexandr V.

## List Total Colouring Conjecture ★★

Author(s): Borodin; Kostochka; Woodall

**Conjecture**If is the total graph of a multigraph, then .

Keywords: list coloring; Total coloring; total graphs

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

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

**Conjecture**Every planar graph is acyclically 5-choosable.

Keywords:

## The Borodin-Kostochka Conjecture ★★

**Conjecture**Every graph with maximum degree has chromatic number at most .

Keywords:

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

**Conjecture**A triangle-free graph with maximum degree has chromatic number at most .

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