Abstract
In what follows we prove that a finite graph of n nodes in which each node has degree ≥ 1 but ≤ possesses a set of at least n/(1 + ) pairwise disjoint edges. Our principal theorem states an analogue of this result for the case when each node has degree ≥2: we show that in this case the graph possesses a set of at least 2n/(2 + max(4, )) mutually disjoint edges.
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