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Parity balance of the $i$-th dimension edges in Hamiltonian cycles of the hypercube
Hypercube Hamiltonian cycles i-th dimension edges equi-independence number
2010/9/20
Let n 2 be an integer, and let i 2 f0; : : : ; n 1g. An i-th dimension edge in the n-dimensional hypercube Qn is an edge v1v2 such that v1; v2 di er just at their i-th entries. The parity...
We prove that if Cay(G; S) is a connected Cayley graph with n vertices, and the prime factorization of n is very small, then Cay(G; S) has a hamiltonian cycle. More precisely, if p, q, and r are disti...