Abstract
We study conditions under which the treewidth of three different classes of random graphs is linear in the number of vertices. For the Erdős–Rényi random graph G(n,m), our result improves a previous lower bound obtained by Kloks (1994) [22]. For random intersection graphs, our result strengthens a previous observation on the treewidth by Karoński et al. (1999) [19]. For scale-free random graphs based on the Barabási-Albert preferential-attachment model, it is shown that if more than 11 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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