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.
"The Maximal Length of 2-Path in Random Critical Graphs." J. Appl. Math. 2018 1 - 5, 2018. https://doi.org/10.1155/2018/8983218