The classical global criteria for the existence of Hamilton cycles only apply to graphs with large edge density and small diameter. In a series of papers Asratian and Khachatryan developed local criteria for the existence of Hamilton cycles in finite connected graphs, which are analogues of the classical global criteria due to Dirac (1952), Ore (1960), Jung (1978), and Nash-Williams (1971). The idea was to show that the global concept of Hamiltonicity can, under rather general conditions, be captured by local phenomena, using the structure of balls of small radii. (The ball of radius r centered at a vertex u is a subgraph of G induced by the set of vertices whose distances from u do not exceed r.) Such results are called localization theorems and present a possibility to extend known classes of finite Hamiltonian graphs.

In this paper we formulate a general approach for finding localization theorems and use this approach to formulate local analogues of well-known results of Bauer et al. (1989), Bondy (1980), Häggkvist and Nicoghossian (1981), and Moon and Moser (1963). Finally we extend two of our results to infinite locally finite graphs and show that they guarantee the existence of Hamiltonian curves, introduced by Kündgen, Li and Thomassen (2017).

Hamilton循环存在的经典全局准则仅适用于具有大边密度和小直径的图。在一系列论文中，Asratian和Khachatryan为有限连通图中的汉密尔顿循环的存在开发了局部准则，这是由于Dirac（1952），Ore（1960），Jung（1978）和Nash-威廉姆斯（1971）。这个想法是要表明，在相当普遍的条件下，可以通过使用小半径的球的结构来捕获局部现象来捕获全球汉密尔顿性概念。（半径的球- [R为中心在顶点ü是的子图G ^由该组顶点的距离，其从诱导ü不超过ř。）这样的结果称为定位定理，并提供了扩展有限哈密顿图的已知类别的可能性。

在本文中，我们制定了一种寻找定位定理的通用方法，并使用该方法来制定Bauer等人的著名结果的局部类似物。（1989年），邦迪（1980年），黑格维斯特（Häggkvist）和尼古斯（Nicoghossian）（1981年）和月亮与摩泽尔（1963年）。最后，我们将我们的两个结果扩展到无限局部有限图，并表明它们保证了汉密尔顿曲线的存在，这由Kündgen，Li和Thomassen（2017）提出。