Abstract
Consider the subset graph G( n,k) whose vertex set C( n,k) is the set of all n-tuples of ‘0's’ and ‘1's’ with exactly k ‘1's’. Let an edge exist between two vertices a and b in G( n,k) if and only if a can be transformed into b by the interchange of two adjacent coordinate values, with the first and last coordinates considered adjacent. This paper shows that a Hamiltonian circuit exists in G( n,k) if and only if neither n and k are both even, nor k=2 or n−2 for n>7. It is also shows that a Hamiltonian path exists in G( n,k) if and only if n and k are not both even. Such Hamiltonian paths and circuits are called ‘Gray codes’ of C( n,k).
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