List Colouring Squares of Planar Graphs

Details List Colouring Squares of Planar Graphs List Colouring Squares of Planar Graphs

2008-07-21

arxiv.org/abs/0807.3233v1

Mathematics

Combinatorics

29 pages, also available at http://www.cdam.lse.ac.uk/Reports/Files/cdam-2008-09.pdf

Scientific paper

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.

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