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2018 The Maximal Length of 2-Path in Random Critical Graphs
Vonjy Rasendrahasina, Vlady Ravelomanana, Liva Aly Raonenantsoamihaja
J. Appl. Math. 2018: 1-5 (2018). DOI: 10.1155/2018/8983218

Abstract

Given a graph, its 2 -core is the maximal subgraph of G without vertices of degree 1 . A 2 -path in a connected graph is a simple path in its 2 -core such that all vertices in the path have degree 2 , except the endpoints which have degree 3 . Consider the Erdős-Rényi random graph G ( n , M ) built with n vertices and M edges uniformly randomly chosen from the set of n 2 edges. Let ξ n , M be the maximum 2 -path length of G ( n , M ) . In this paper, we determine that there exists a constant c ( λ ) such that E ξ n , n / 2 1 + λ n - 1 / 3 ~ c ( λ ) n 1 / 3 , f o r a n y r e a l λ . This parameter is studied through the use of generating functions and complex analysis.

Citation

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Vonjy Rasendrahasina. Vlady Ravelomanana. Liva Aly Raonenantsoamihaja. "The Maximal Length of 2-Path in Random Critical Graphs." J. Appl. Math. 2018 1 - 5, 2018. https://doi.org/10.1155/2018/8983218

Information

Received: 1 December 2017; Accepted: 3 April 2018; Published: 2018
First available in Project Euclid: 13 June 2018

zbMATH: 07132109
MathSciNet: MR3806007
Digital Object Identifier: 10.1155/2018/8983218

Rights: Copyright © 2018 Hindawi

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