Name
Abstract | ||
|---|---|---|
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 B. 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 @?\"@a\"@?\"E\"(\"X\")f(@a) 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 B. Alspach, S.C. Locke, and D. Witte, for the case where X is cubic, or has an odd number of vertices. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1016/j.disc.2005.02.020 | Discrete Mathematics |
Keywords | Field | DocType |
circulant graph,abelian group,cayley graph,flow,hamiltonian cycle | Discrete mathematics,Abelian group,Combinatorics,Circulant graph,Vertex (geometry),Hamiltonian path,Cayley graph,Cycle graph,Connectivity,Finite group,Mathematics | Journal |
Volume | Issue | ISSN |
299 | 1-3 | Discrete Mathematics |
Citations | PageRank | References |
0 | 0.34 | 3 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Dave Witte Morris | 1 | 20 | 5.42 |
| Joy Morris | 2 | 78 | 16.06 |
| David Petrie Moulton | 3 | 11 | 3.38 |