论文标题
随机apollonian网络中的韧性和汉密尔顿
Toughness and Hamiltonicity in Random Apollonian Networks
论文作者
论文摘要
在本文中，我们研究了随机的Apollonian网络（RANS）的韧性，这是一个随机图模型，该模型生成具有幂律特性的平面图。我们认为它们的重要特征：每次运行都是一个独特代表的和弦图，平面$ 3 $ -tree，因此，有关这些类别的已知结果可以得到特定。我们在八个非平凡的子类中建立了班级的分区，对于这些子类中的每一个，我们为元素的韧性提供了界限。我们还研究了这些子类元素的大麻性。
In this paper we study the toughness of Random Apollonian Networks (RANs), a random graph model which generates planar graphs with power-law properties. We consider their important characteristics: every RAN is a uniquely representable chordal graph and a planar $3$-tree and as so, known results about these classes can be particularized. We establish a partition of the class in eight nontrivial subclasses and for each one of these subclasses we provide bounds for the toughness of their elements. We also study the hamiltonicity of the elements of these subclasses.
