# complete multipartite graph

## List Colourings of Complete Multipartite Graphs with 2 Big Parts ★★

Author(s): Allagan

\begin{question} Given $a,b\geq2$, what is the smallest integer $t\geq0$ such that $\chi_\ell(K_{a,b}+K_t)= \chi(K_{a,b}+K_t)$? \end{question}

## Choice number of complete multipartite graphs with parts of size 4 ★

Author(s):

\begin{question} What is the choice number of $K_{4*k}$ for general $k$? \end{question}

## Choice Number of k-Chromatic Graphs of Bounded Order ★★

Author(s): Noel

\begin{conjecture} If $G$ is a $k$-chromatic graph on at most $mk$ vertices, then $\text{ch}(G)\leq \text{ch}(K_{m*k})$. \end{conjecture}

## Ohba's Conjecture ★★

Author(s): Ohba

\begin{conjecture} If $|V(G)|\leq 2\chi(G)+1$, then $\chi_\ell(G)=\chi(G)$. \end{conjecture}