Longest cycles in sparse random digraphs


Long paths and cycles in sparse random graphs and digraphs were studied intensively in the 1980’s. It was finally shown by Frieze in 1986 that the random graph G(n, p) with p = c/n has a cycle on at all but at most (1 + ε)ce−cn vertices with high probability, where ε = ε(c) → 0 as c → ∞. This estimate on the number of uncovered vertices is essentially tight… (More)
DOI: 10.1002/rsa.20435