Approximate Counting of Graphical Realizations

@inproceedings{Erds2015ApproximateCO,
  title={Approximate Counting of Graphical Realizations},
  author={P{\'e}ter L. Erdős and S{\'a}ndor Z. Kiss and Istv{\'a}n Mikl{\'o}s and Lajos Soukup and Arndt von Haeseler},
  booktitle={PloS one},
  year={2015}
}
In 1999 Kannan, Tetali and Vempala proposed a MCMC method to uniformly sample all possible realizations of a given graphical degree sequence and conjectured its rapidly mixing nature. Recently their conjecture was proved affirmative for regular graphs (by Cooper, Dyer and Greenhill, 2007), for regular directed graphs (by Greenhill, 2011) and for half-regular bipartite graphs (by Miklós, Erdős and Soukup, 2013). Several heuristics on counting the number of possible realizations exist (via… CONTINUE READING
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A remark on the existence of finite graphs

V. Havel
(in Czech),Časopis Pěst. Mat • 1955
View 12 Excerpts
Highly Influenced

On graphical degree sequences and realizations, Combinatorics, Probability and Computing

P. L. Erdős, Z. Király, I. Miklós
July 10, • 2013
View 4 Excerpts
Highly Influenced

Combinatorial properties of matrices of zeros and ones, Canad

H J.Ryser
J. Math • 1957
View 2 Excerpts
Highly Influenced

On graphical degree sequences and realizations

Z. Király, I Miklós
Combinatorics , Probability and Computing • 2013

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