List Colouring Squares of Planar Graphs

Frédéric Havet; Jan van den Heuvel; Colin McDiarmid; Bruce Reed

List Colouring Squares of Planar Graphs

Combinatorics 2017-05-16 v2

Authors: Frédéric Havet , Jan van den Heuvel , Colin McDiarmid , Bruce Reed

Abstract

In 1977, Wegner conjectured that the chromatic number of the square of every planar graph $G$ with maximum degree $\Delta\ge8$ is at most $\bigl\lfloor\frac32\Delta\bigr\rfloor+1$ . We show that it is at most $\frac32 \Delta (1+o(1))$ (where the $o(1)$ is as $\Delta\to+\infty$ ), and indeed that this is true for the list chromatic number and for more general classes of graphs.

Keywords

graph coloring ramsey theory and colorings

Cite

@article{arxiv.0807.3233,
  title  = {List Colouring Squares of Planar Graphs},
  author = {Frédéric Havet and Jan van den Heuvel and Colin McDiarmid and Bruce Reed},
  journal= {arXiv preprint arXiv:0807.3233},
  year   = {2017}
}

Comments

34 pages

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