2 research outputs found
Flows that are sums of hamiltonian cycles in Cayley graphs on abelian groups
If X is any connected Cayley graph on any finite abelian group, we determine
precisely which flows on X can be written as a sum of hamiltonian cycles. (This
answers a question of Brian Alspach.) In particular, if the degree of X is at
least 5, and X has an even number of vertices, then the flows that can be so
written are precisely the even flows, that is, the flows f, such that the sum
of the edge-flows of f is divisible by 2. On the other hand, there are examples
of degree 4 in which not all even flows can be written as a sum of hamiltonian
cycles. Analogous results were already known, from work of Alspach, Locke, and
Witte, for the case where X is cubic, or has an odd number of vertices.Comment: Latex2e file, 68 pages, minor errors corrected and title slightly
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