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arXiv · 0907.5481

Treewidth of Erdös-Rényi Random Graphs, Random Intersection Graphs, and Scale-Free Random Graphs

Yong Gao
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Abstract

We prove that the treewidth of an Erdös-Rényi random graph $\rg{n, m}$ is, with high probability, greater than $βn$ for some constant $β> 0$ if the edge/vertex ratio $\frac{m}{n}$ is greater than 1.073. Our lower bound $\frac{m}{n} > 1.073$ improves the only previously-known lower bound. We also study the treewidth of random graphs under two other random models for large-scale complex networks. In particular, our result on the treewidth of \rigs strengths a previous observation on the average-case behavior of the \textit{gate matrix layout} problem. For scale-free random graphs based on the Barabási-Albert preferential-attachment model, our result shows that if more than 12 vertices are attached to a new vertex, then the treewidth of the obtained network is linear in the size of the network with high probability.

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Yong Gao. 2009-07-31. Treewidth of Erdös-Rényi Random Graphs, Random Intersection Graphs, and Scale-Free Random Graphs. https://arxiv.org/abs/0907.5481

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