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- W1967041330 abstract "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))." @default.
- W1967041330 created "2016-06-24" @default.
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- W1967041330 date "2005-01-23" @default.
- W1967041330 modified "2023-09-26" @default.
- W1967041330 title "Finding large cycles in Hamiltonian graphs" @default.
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- W1967041330 doi "https://doi.org/10.5555/1070432.1070456" @default.
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