Cubic graphs on n vertices with a separating matching have one of size at least n/2 - 2, with exact n/2 for claw-free cases and near n/2 for bipartite under a conjecture.
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Separating Matchings in Cubic Graphs
Cubic graphs on n vertices with a separating matching have one of size at least n/2 - 2, with exact n/2 for claw-free cases and near n/2 for bipartite under a conjecture.