随机几何图中的Hamilton圈
Hamilton cycles in random geometric graphs
摘要：
我们证明了，在吉尔伯特模型的随机几何图，几乎每一个图成为哈密尔顿正是当它第一次成为2-连通。这回答了彭罗斯的一个问题。我们还证明了在k-近邻模型中，存在一个常数κ使得几乎每个κ-连通图都有一个Hamilton圈.
英文摘要：
We prove that, in the Gilbert model for a random geometric graph, almost every graph becomes Hamiltonian exactly when it first becomes 2-connected. This answers a question of Penrose. We also show that in the k-nearest neighbor model, there is a constant κ such that almost every κ-connected graph has a Hamilton cycle.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
