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  1. ; ; (, SIAM journal on discrete mathematics)
    We study the Hamiltonicity of the following model of a random graph. Suppose that we partition $[n]$ into $$V_1,V_2,\ldots,V_k$$ and add edge $$\{x,y\}$$ to our graph with probability $$p$$ if there exists $$i$$ such that $$x,y\in V_i$$. Otherwise, we add the edge with probability $$q$$. 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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