On the Achromatic Number of Hypercubes

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The achromatic number of a finite graph G, ψ(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<c1<c2, independent of m, such that c1(m2m-1)1/2≤ψ(Pm 2)≤c2(m2m-1)1/2.

Original languageEnglish
Pages (from-to)177-182
Number of pages6
JournalJournal of Combinatorial Theory. Series B
Issue number2
StatePublished - Jul 2000

Bibliographical note

Funding Information:
1Supported in part by the Israel Science Foundation and by internal research grants from Bar-Ilan University.


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