On a greedy 2‐matching algorithm and Hamilton cycles in random graphs with minimum degree at least three

We describe and analyse a simple greedy algorithm 2greedy that finds a good 2-matching M in the random graph G=Gn,cni¾?i¾?3 when ci¾?10. A 2-matching is a spanning subgraph of maximum degree two and G is drawn uniformly from graphs with vertex set [n], cn edges and minimum degree at least three. By good we mean that M has Ologn components. We then use this 2-matching to build a Hamilton cycle in On1.5+o1 time w.h.p. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 45, 443-497, 2014

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