T
Tomasz Łuczak
Researcher at Adam Mickiewicz University in Poznań
Publications - 165
Citations - 7679
Tomasz Łuczak is an academic researcher from Adam Mickiewicz University in Poznań. The author has contributed to research in topics: Random graph & Random regular graph. The author has an hindex of 37, co-authored 164 publications receiving 7147 citations. Previous affiliations of Tomasz Łuczak include Wrocław University of Technology & Emory University.
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The birth of the giant component
TL;DR: In this paper, the authors derived the limiting distributions for the sparse connected components that are present when a random graph on n vertices has approximately 1/2n edges, and showed that such a graph consists entirely of trees, unicyclic components, and bicyclic components with probability approaching √2/3 cosh √5/18 ≈ 0.9957; the limiting probability that it is planar lies between 0.987 and 0.9325 as n∞.
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The birth of the giant component
TL;DR: A “uniform” model of random graphs, which allows self-loops and multiple edges, is shown to lead to formulas that are substanitially simpler than the analogous formulas for the classical random graphs of Erdos and Renyi.
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Edge weights and vertex colours
TL;DR: In this paper, the edges of any non-trivial graph can be assigned weights from {1, 2, 3} so that adjacent vertices have different sums of incident edge weights.