Coloring the square of the Cartesian product of two cycles

@article{Sopena2010ColoringTS,
title={Coloring the square of the Cartesian product of two cycles},
author={{\'E}ric Sopena and Jiaojiao Wu},
journal={Discrete Mathematics},
year={2010},
volume={310},
pages={2327-2333}
}

The square G2 of a graph G is defined on the vertex set of G in such a way that distinct vertices with distance at most two in G are joined by an edge. We study the chromatic number of the square of the Cartesian product Cm2Cn of two cycles and show that the value of this parameter is at most 7 except when m = n = 3, in which case the value is 9, and when m = n = 4 or m = 3 and n = 5, in which case the value is 8. Moreover, we conjecture that for every G = Cm2Cn, the chromatic number of G2… CONTINUE READING