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The square G2 of a graph G is obtained from G by adding edges joining all pairs of nodes at distance 2 in G. In this note we prove that χ((Cm□Cn)2)≤6 for m,n≥40. This confirms Conjecture 19 stated in [É. Sopena, J. Wu, Coloring the square of the Cartesian product of two cycles, Discrete Math. 310 (2010) 2327–2333].
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