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Two edge-disjoint hamiltonian cycles in the butterfly graph. (English) Zbl 0807.05047
A graph is called a butterfly graph of dimension \(n\) if it is the set of couples \((a; x_{n-1}\ldots x_ 0)\), where \(a\in \{0,\dots,n- 1\}\) and \(x_ i\in \{0,1\}\) for all \(i\in \{0,\dots,n- 1\}\), and \([(a;x_{n- 1}\ldots x_ 0)\), \((a';x_{n-1}'\ldots x_ 0')]\) is an edge of the graph if \(a'\equiv a+1\pmod n\) and if \(x_ i= x_ i'\) for all \(i\neq a'\). The paper shows that the butterfly graph contains two edge-disjoint hamiltonian cycles. It also gives a recursive method for constructing these cycles.
Reviewer: W.K.Chen (Chicago)

MSC:
05C45 Eulerian and Hamiltonian graphs
05C38 Paths and cycles
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