An almost linear time algorithm for finding Hamilton cycles in sparse random graphs with minimum degree at least three - Frieze, Alan; Haber, Simi (Random structures & algorithms, 2015)
We describe an algorithm for finding Hamilton cycles in random graphs. Our model is the random graph G=Gn,mδ≥3. In this model G is drawn uniformly from graphs with vertex set [n], m edges and minimum degree at least three. We focus on the case where m = cn for constant c. If c is sufficiently large then our algorithm runs in O(n1+o(1)) time and succeeds w.h.p. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 73–98, 2015