A parity digraph has a kernel


We show that every digraph has a kernel (i.e. an absorbing and independent set) under the following parity condition: For every pair of verticesx, y x ≠ y all minimal directed paths betweenx andy have the same length parity.

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Blidia, M. A parity digraph has a kernel. Combinatorica 6, 23–27 (1986). https://doi.org/10.1007/BF02579405

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