Abstract
We prove that the number of Hamilton cycles in the random graph G(n, p) is n!pn(1+ o(1))n asymptotically almost surely (a.a.s.), provided that p ≥ ln n+ln ln n+ω(1)/n. Furthermore, we prove the hitting time version of this statement, showing that in the random graph process, the edge that creates a graph of minimum degree 2 creates (ln n/e) n(1 + o(1))n Hamilton cycles a.a.s.
Original language | English |
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Pages (from-to) | 27-42 |
Number of pages | 16 |
Journal | SIAM Journal on Discrete Mathematics |
Volume | 27 |
Issue number | 1 |
DOIs | |
State | Published - 2013 |
Keywords
- Hamilton cycles
- Number of Hamilton cycles
- Random graphs