Toughness and Hamiltonicity in Random Apollonian Networks
Combinatorics
2020-02-24 v1
Abstract
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 -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.
Keywords
Cite
@article{arxiv.2002.09244,
title = {Toughness and Hamiltonicity in Random Apollonian Networks},
author = {Lilian Markenzon and Christina F. E. M. Waga},
journal= {arXiv preprint arXiv:2002.09244},
year = {2020}
}
Comments
15 pages, 5 figures