Abstract
We give a randomized algorithm that determines if a given graph has a simple path of length at least k in O ( 2 k ⋅ poly ( n ) ) time. Our method extends a recent O ( 2 3 k / 2 ⋅ poly ( n ) ) ⩽ O ( 2.83 k ⋅ poly ( n ) ) algorithm of Koutis.
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