%0 Journal Article
%T List Colouring Squares of Planar Graphs
%A Fr¨¦d¨¦ric Havet
%A Jan van den Heuvel
%A Colin McDiarmid
%A Bruce Reed
%J Mathematics
%D 2008
%I arXiv
%X In 1977, Wegner conjectured that the chromatic number of the square of every planar graph $G$ with maximum degree $\Delta\ge8$ is at most $\lfloor\frac32 \Delta\bigr+1$. We show that it is at most $\frac32 \Delta (1+o(1))$, and indeed this is true for the list chromatic number and for more general classes of graphs.
%U http://arxiv.org/abs/0807.3233v1