A note on treewidth in random graphs

Authors:
Chaoyi Wang;Tian Liu;Peng Cui;Ke Xu
Affiliations:
Ministry of Education, Institute of Software, School of Electronic Engineering and Computer Science, Peking University, Beijing, China;Ministry of Education, Institute of Software, School of Electronic Engineering and Computer Science, Peking University, Beijing, China;School of Information Resource Management, Renmin University of China, Beijing, China;National Laboratory of Software Development Environment, Beihang University, Beijing, China
Venue:
COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
Year:
2011

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Abstract

We show that in Erdös-Rényi random graph G(n, p) with high probability, when p = c/n and c is a constant, the treewidth is upper bounded by tn for some constant t c, but when p ≫ 1/n, the treewidth is lower bounded by n - o(n). The upper bound refutes a conjecture that treewidth in G(n, p = c/n) is as large as n - o(n), and the lower bound provides further theoretical evidence on hardness of some random constraint satisfaction problems called Model RB and Model RD.