On the number of Hamilton cycles in sparse random graphs

Roman Glebov; Michael Krivelevich

doi:10.1137/120884316

On the number of Hamilton cycles in sparse random graphs

Roman Glebov, Michael Krivelevich

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

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
Pages (from-to)	27-42
Number of pages	16
Journal	SIAM Journal on Discrete Mathematics
Volume	27
Issue number	1
DOIs	https://doi.org/10.1137/120884316
State	Published - 2013

Keywords

Hamilton cycles
Number of Hamilton cycles
Random graphs

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1137/120884316

Cite this

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AB - 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.

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On the number of Hamilton cycles in sparse random graphs

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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