Lecturer: Alistair Sinclair Based on Scribe Notes By: 14.1 Finding Hamilton Cycles in Random Graphs
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چکیده
Moreover, there is a polynomial time algorithm to find a Hamilton cycle in a random graph G ∈ Gn,p w.h.p. for all p > lnn+ln lnn+c(n) n , c(n) → ∞ [BFF85]. In this section, we look at a simpler algorithm [AV77] that works for all p ≥ c lnn n−1 for a sufficiently large constant c. This is a slightly weaker result as the value of c, determined by Chernoff bound arguments used in the algorithm’s analysis, is greater than 1. Note that as a by-product, this algorithm shows that a Hamilton cycle exists in such graphs w.h.p..
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