# On the Achromatic Number of Hypercubes

@article{Roichman2000OnTA,
title={On the Achromatic Number of Hypercubes},
author={Yuval Roichman},
journal={J. Comb. Theory, Ser. B},
year={2000},
volume={79},
pages={177-182}
}
The achromatic number of a finite graph G, ?(G), is the maximum number of independent sets into which the vertex set may be partitioned, so that between any two parts there is at least one edge. For an m-dimensional hypercube Pm2 we prove that there exist constants 0
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It is shown that the problem of determining the achromatic number of a tree is NP-hard, and it is proved that almost all trees T satisfy ψ(T ) = q(m), where m is the number of edges in T .

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