Directed graphs, Hamiltonicity and doubly stochastic matrices

By Vivek Shripad Borkar, V. Ejov, J. Filar. 2004

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Poisson Cloning Model for Random Graphs (2008, unknown): “Repeating this k − 1 times, we have Λi+1 = Λi(1 − TUi−1)(1 − TUi−2) · · · (1 − TUi−k+1), and hence Λi+1 = Λi(1 − TUi−1) · · · (1 − TUi−k+1) = Λi−1(1 − TUi−1−1) · · · (1 − TUi−1−k+1) · (1 − TUi−1) · · · (1 − TUi−k+1) = λ Nλ−(i+1)k+1 ∏ j=Nλ−1 k∤Nλ−j ( 1 − Tj ) .”
The k-orientability thresholds for Gn, p (2007, background): “The k-core thresholds for random graphs have been studied in [20, 4, 15, 7, 10].”
A simple solution to the k-core problem (2007, methodology): “See Fernholz and Ramachandran [7, 8] and in particular Cooper [ 3 ] for similar results.”
Distribution of subgraphs of random regular graphs (2008, methodology): “The goal is either to avoid creation of a giant component (of size (n)) for as long as possible [4, 5 , 6, 15] or to create a giant as soon as possible [7, 11].”
Asymptotic normality of the k-core in random graphs (2006, background): “ginal in pagination and typographic detail. 1 2 S. JANSON AND M. J. LUCZAK studying the k-core of a random graph with a speciﬁed degree sequence, for example, Fernholz and Ramachandran [8, 9], Cooper [6], Molloy [23] (the last two references also consider hypergraphs) and Janson and Luczak [17]. Fur”