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Creators/Authors contains: "Anastos, Michael"

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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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  2. ; ; (, The Electronic journal of combinatorics)
    Let Ωq denote the set of proper [q]-colorings of the random graph Gn,m,m=dn/2 and let Hq be the graph with vertex set Ωq and an edge {σ,τ} where σ,τ are mappings [n]→[q] iff h(σ,τ)=1. Here h(σ,τ) is the Hamming distance |{v∈[n]:σ(v)≠τ(v)}|. We show that w.h.p. Hq contains a single giant component containing almost all colorings in Ωq if d is sufficiently large and q≥cdlogd for a constant c>3/2. 
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    Accepted Manuscript Full Text Available