\input zb-basic
\input zb-ioport
\iteman{io-port 05888524}
\itemau{Kostochka, Alexandr V.; Stiebitz, Michael; Woodall, Douglas R.}
\itemti{Ohba's conjecture for graphs with independence number five.}
\itemso{Discrete Math. 311, No. 12, 996-1005 (2011).}
\itemab
Summary: Ohba has conjectured that if $G$ is a $k$-chromatic graph with at most $2k+1$ vertices, then the list chromatic number or choosability ch$(G)$ of $G$ is equal to its chromatic number $\chi (G)$, which is $k$. It is known that this holds if $G$ has independence number at most three. It is proved here that it holds if $G$ has independence number at most five. In particular, and equivalently, it holds if $G$ is a complete $k$-partite graph and each part has at most five vertices.
\itemrv{~}
\itemcc{}
\itemut{chromatic number; vertex coloring; list coloring; list chromatic number; choosability; complete multipartite graph}
\itemli{doi:10.1016/j.disc.2011.02.026}
\end