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A graph $G$ with two $K_6$ subgraphs, in which any one-factor of $G$ induces a one-factor in exactly one of the $K_6$ subgraphs?
I'm seeking a simple graph $G$ of the following type:
It contains two disjoint copies of $K_6$ (the complete graph on 6 nodes), $H$ and $H'$ say.
Any one-factor of $G$ must contain either (a) a one ...
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