The Maximal Length of 2-Path in Random Critical Graphs

Vonjy Rasendrahasina, Vlady Ravelomanana and Liva Aly Raonenantsoamihaja

Journal of Applied Mathematics, 2018, vol. 2018, 1-5

Abstract:

Given a graph, its -core is the maximal subgraph of without vertices of degree . A -path in a connected graph is a simple path in its -core such that all vertices in the path have degree , except the endpoints which have degree . Consider the Erdős-Rényi random graph built with vertices and edges uniformly randomly chosen from the set of edges. Let be the maximum -path length of . In this paper, we determine that there exists a constant such that This parameter is studied through the use of generating functions and complex analysis.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:8983218

DOI: 10.1155/2018/8983218

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