Cranston and Kim conjectured that if $G$ is a connected graph with maximum degree $\Delta$ and $G$ is not a Moore Graph, then $\chi_{\ell}(G^2)\le \Delta^2-1$; here $\chi_{\ell}$ is the list chromatic number. We prove their conjecture; in fact, we show that this upper bound holds even for online list chromatic number.
@article{10_37236_4978,
author = {Daniel W. Cranston and Landon Rabern},
title = {Painting squares in {\(\Delta^2-1\)} shades},
journal = {The electronic journal of combinatorics},
year = {2016},
volume = {23},
number = {2},
doi = {10.37236/4978},
zbl = {1339.05124},
url = {http://geodesic.mathdoc.fr/articles/10.37236/4978/}
}
TY - JOUR
AU - Daniel W. Cranston
AU - Landon Rabern
TI - Painting squares in \(\Delta^2-1\) shades
JO - The electronic journal of combinatorics
PY - 2016
VL - 23
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/4978/
DO - 10.37236/4978
ID - 10_37236_4978
ER -
%0 Journal Article
%A Daniel W. Cranston
%A Landon Rabern
%T Painting squares in \(\Delta^2-1\) shades
%J The electronic journal of combinatorics
%D 2016
%V 23
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/4978/
%R 10.37236/4978
%F 10_37236_4978
Daniel W. Cranston; Landon Rabern. Painting squares in \(\Delta^2-1\) shades. The electronic journal of combinatorics, Tome 23 (2016) no. 2. doi: 10.37236/4978
