On Pósa's Conjecture for Random Graphs
نویسندگان
چکیده
The famous Pósa conjecture states that every graph of minimum degree at least 2n/3 contains the square of a Hamilton cycle. This has been proved for large n by Komlós, Sarközy and Szemerédi. Here we prove that if p ≥ n−1/2+ε, then asymptotically almost surely, the binomial random graph Gn,p contains the square of a Hamilton cycle. This provides an ‘approximate threshold’ for the property in the sense that the result fails to hold if p ≤ n−1/2.
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ورودعنوان ژورنال:
- SIAM J. Discrete Math.
دوره 26 شماره
صفحات -
تاریخ انتشار 2012