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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TLDR
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 .

The harmonious chromatic number and the achromatic number

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TLDR
The achromatic number of the Cartesian product of graphs G 1 and G 2 is studied and the bounds give the exact a chromatic numbers W(Krn X Kn} if not both m and n are equal to 2.

Coding Theory