List Colouring When The Chromatic Number Is Close To the Order Of The Graph

Ohba has conjectured [7] that if G has 2χ(G)+1 or fewer vertices then the list chromatic number and chromatic number of G are equal. In this short note we prove the weaker version of the conjecture obtained by replacing 2χ(G)+1 by $$ \frac{5} {3}\chi {\left( G \right)} - \frac{4} {3}. $$