Finding paths and cycles of superpolylogarithmic length
Harold N. Gabow · 2004
Let l be the number of edges in a longest cycle containing a given vertex v in an undirected graph. We show how to find a cycle through v of length (Ω(√ log l, log log l)) in polynomial time. This implies the same bound for the longest cycle, longest vw-path and longest path. The previous best bound for longest path is length Ω((log l )2/, log log l) due to Björklund and Husfeldt. Our approach, which builds on Björklund and Husfeldt's, uses cycles to enlarge cycles. This self-reducibility allows the approximation method to be iterated.