Finding paths and cycles of superpolylogarithmic length
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Finding large cycles in Hamiltonian graphs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
On a simple randomized algorithm for finding a 2-factor in sparse graphs
Information Processing Letters
Approximating the maximum clique minor and some subgraph homeomorphism problems
Theoretical Computer Science
Algorithms for long paths in graphs
Theoretical Computer Science
ACM Transactions on Algorithms (TALG)
Degree-Constrained Subgraph Problems: Hardness and Approximation Results
Approximation and Online Algorithms
Longest Path Problems on Ptolemaic Graphs
IEICE - Transactions on Information and Systems
Not being (super)thin or solid is hard: A study of grid Hamiltonicity
Computational Geometry: Theory and Applications
On a simple randomized algorithm for finding a 2-factor in sparse graphs
Information Processing Letters
Finding large cycles in Hamiltonian graphs
Discrete Applied Mathematics
Algorithm for two disjoint long paths in 2-connected graphs
Theoretical Computer Science
Paired approximation problems and incompatible inapproximabilities
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
A linear-time algorithm for the longest path problem in rectangular grid graphs
Discrete Applied Mathematics
Approximating the longest cycle problem on graphs with bounded degree
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Efficient algorithms for the longest path problem
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
On the approximability of some degree-constrained subgraph problems
Discrete Applied Mathematics
An efficient parallel algorithm for the longest path problem in meshes
The Journal of Supercomputing
Computing and counting longest paths on circular-arc graphs in polynomial time
Discrete Applied Mathematics
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We consider the problem of finding a long, simple path in an undirected graph. We present a polynomial-time algorithm that finds a path of length $\Omega\bigl((\log L/\log\log L)^2\bigr)$, where L denotes the length of the longest simple path in the graph. This establishes the performance ratio O(n(log log n/log n)2) for the longest path problem, where n denotes the number of vertices in the graph.