Finding paths and cycles of superpolylogarithmic length

Authors:
Harold N. Gabow
Affiliations:
University of Colorado at Boulder, Boulder, CO
Venue:
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Year:
2004

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Abstract

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.