Longest cycles in 3-connected cubic graphs
Journal of Combinatorial Theory Series B
Approximating the minimum degree spanning tree to within one from the optimal degree
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
On the approximation of finding a(nother) hamiltonian cycle in cubic hamiltonian graphs
Journal of Algorithms
Approximating the Longest Cycle Problem in Sparse Graphs
SIAM Journal on Computing
Approximation Through Local Optimality: Designing Networks with Small Degree
Proceedings of the 12th Conference on Foundations of Software Technology and Theoretical Computer Science
Finding a Path of Superlogarithmic Length
SIAM Journal on Computing
Finding paths and cycles of superpolylogarithmic length
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
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
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
The longest path problem is polynomial on cocomparability graphs
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
A linear-time algorithm for the longest path problem in rectangular grid graphs
Discrete Applied Mathematics
On the approximability of some degree-constrained subgraph problems
Discrete Applied Mathematics
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We show how to find in Hamiltonian graphs a cycle of length nΩ(1/log log n). This is a consequence of a more general result in which we show that if G has maximum degree d and has a cycle with k vertices (or a 3-cyclable minor H with k vertices), then we can find in O(n3) time a cycle in G of length kΩ(1/log d). From this we infer that if G has a cycle of length k, then one can find in O(n3) time a cycle of length kΩ(1/(log(n/k)+log log n)), which implies the result for Hamiltonian graphs. Our results improve, for some values of k and d, a recent result of Gabow [8] showing that if G has a cycle of length k, then one can find in polynomial time a cycle in G of length exp(Ω(√log k/log log k)).