Journal of Applied Mathematics

The Maximal Length of 2-Path in Random Critical Graphs

Vonjy Rasendrahasina, Vlady Ravelomanana, and Liva Aly Raonenantsoamihaja

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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.

Article information

J. Appl. Math., Volume 2018 (2018), Article ID 8983218, 5 pages.

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

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

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