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- W239967920 abstract "We show how to find in Hamiltonian graphs a cycle of length n^@W^(^1^/^l^o^g^l^o^g^n^)=exp(@W(logn/loglogn)). This is a consequence of a more general result in which we show that if G has a 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(n^3) time a cycle in G of length k^@W^(^1^/^l^o^g^d^). From this we infer that if G has a cycle of length k, then one can find in O(n^3) time a cycle of length k^@W^(^1^/^(^l^o^g^(^n^/^k^)^+^l^o^g^l^o^g^n^)^), which implies the result for Hamiltonian graphs. Our results improve, for some values of k and d, a recent result of Gabow (2004) [11] showing that if G has a cycle of length k, then one can find in polynomial time a cycle in G of length exp(@W(logk/loglogk)). We finally show that if G has fixed Euler genus g and has a cycle with k vertices (or a 3-cyclable minor H with k vertices), then we can find in polynomial time a cycle in G of length f(g)k^@W^(^1^), running in time O(n^2) for planar graphs." @default.
- W239967920 created "2016-06-24" @default.
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- W239967920 date "2006-01-01" @default.
- W239967920 modified "2023-09-23" @default.
- W239967920 title "Finding large cycles in Hamiltonian graphs." @default.
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