Generalizating path and fan graphs: subcoloring and toughness

Markenzon, Lilian; Waga, Christina Fraga Esteves Maciel

doi:10.1590/s0101-74382014005000004

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“…In [17], bounds to the toughness of k-path graphs, k ≥ 2, were presented. Hence, we can present the following result.…”

Section: Corollary 13mentioning

confidence: 99%

Toughness and Hamiltonicity in Random Apollonian Networks

Markenzon¹,

Waga²

2020

Preprint

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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.

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“…In [17], bounds to the toughness of k-path graphs, k ≥ 2, were presented. Hence, we can present the following result.…”

Section: Corollary 13mentioning

confidence: 99%