Hamiltonicity of random graphs in the stochastic block model
Abstract
We study the Hamiltonicity of the following model of a random graph. Suppose that we partition [n] into V1,V2,...,Vk and add edge x,y to our graph with probability p if there exists i such that x,y∈ Vi. Otherwise, we add the edge with probbability q. We denote this model by G(n, p,q) and give tight results for Hamiltonicity, including a critical window analysis, under various conditions.
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