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Odd sums of long cycles in 2-connected graphs.

  • Mathematics.


Let G be a 2-connected graph with minimum degree d and with at least d + 2 vertices. Suppose that G is not a cycle. Then there is an odd set of cycles, each with length at least d + 1, such that they sum to zero. If G is also non-hamiltonian or bipartite, cycles of length at least $2d$ can be used.

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