In this paper we consider the existence of Hamilton cycles in the random graph . This random graph is chosen uniformly from , the set of graphs with vertex set [n], m edges and minimum degree at least 3. Our ultimate goal is to prove that if m = cn and c > 3/2 is constant then G is Hamiltonian w.h.p. In Frieze (2014), the second author showed that c ≥ 10 is sufficient for this and in this paper we reduce the lower bound to c > 2.662…. This new lower bound is the same lower bound found in Frieze and Pittel (2013) for the expansion of so‐called Pósa sets.

中文翻译：

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随机图中最小度至少为3的汉密尔顿循环：改进的分析

本文考虑随机图中Hamilton环的存在性。此随机图是从，具有顶点集[ n ]，m个边和最小度至少为3的图的集合中均匀选择的。我们的最终目标是证明如果m  =  cn且c  > 3/2是常数，则G为哈密顿WHP在楣（2014），第二作者表明ç  ≥10是足够的，并在本文中，我们减少下界ç  > 2.662 ...。这个新的下界与Frieze和Pittel（2013）在扩展所谓的Pósa集时发现的下界相同。