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Friday, October 17, 2008 |
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Isomorphism theorems for even cycles and even cuts in graphs |
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A seminal result of Whitney characterizes when two graphs have the
same cycle space (or equivalently the same cut space): namely,
this occurs exactly when one graph can be obtained from the other by
repeatedly rearranging the graph along one and two vertex cut sets in
a special way. We generalize this result to even cycles in signed graphs
as well as to even cuts in grafts. |