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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
##### Keywords:
butterfly graph; hamiltonian cycles
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