# Connectivity Thresholds for Bounded Size Rules

@article{Einarsson2014ConnectivityTF, title={Connectivity Thresholds for Bounded Size Rules}, author={H. Einarsson and J. Lengler and K. Panagiotou and Frank Mousset and A. Steger}, journal={arXiv: Probability}, year={2014} }

In an Achlioptas process, starting with a graph that has n vertices and no edge, in each round $d \geq 1$ edges are drawn uniformly at random, and using some rule exactly one of them is chosen and added to the evolving graph. For the class of Achlioptas processes we investigate how much impact the rule has on one of the most basic properties of a graph: connectivity. Our main results are twofold. First, we study the prominent class of bounded size rules, which select the edge to add according… Expand

#### One Citation

Randomized Algorithms and Probabilistic Methods: Advanced Topics

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For this, we use the canonical paths method. Thus, we should start by defining paths between any two elements A,B ∈ Ω. It turns out that the exact definition of the paths is not really all that… Expand

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