Journal of Applied Mathematics
- J. Appl. Math.
- Volume 2018 (2018), Article ID 8983218, 5 pages.
The Maximal Length of 2-Path in Random Critical Graphs
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.
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. https://projecteuclid.org/euclid.jam/1528855298