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is an odd-length path or cycle, with the first in the sequence being a cycle, each path in the sequence having both endpoints but no interior points on vertices in previous subgraphs, and each cycle other than the first in the sequence having exactly one vertex in previous subgraphs. For instance, the graph in the illustration may be partitioned in this way into a cycle of five edges and a path of three edges. In the case that a near-perfect matching

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