On March 14, 2022, Tuan Anh Do (Tuấn Anh Đỗ) from the Graz University of Technology / IBS Discrete Mathematics Group gave a talk at the Discrete Math Seminar on rank-width and tree-width of graphs of supercritical random graphs at the Discrete Math Seminar. The title of his talk was “Rank- and tree-width of supercritical random graphs“.
It is known that the rank- and tree-width of the random graph $G(n,p)$ undergo a phase transition at $p = 1/n$; whilst for subcritical $p$, the rank- and tree-width are bounded above by a constant, for supercritical $p$, both parameters are linear in $n$. The known proofs of these results use as a black box an important theorem of Benjamini, Kozma, and Wormald on the expansion of supercritical random graphs. We give a new, short, and direct proof of these results, leading to more explicit bounds on these parameters, and also consider the rank- and tree-width of supercritical random graphs closer to the critical point, showing that this phase transition is smooth.
This is joint work with Joshua Erde and Mihyun Kang.
The IBS Discrete Mathematics Group welcomes Tuan Anh Do (Tuấn Anh Đỗ), a visiting graduate student from the Graz University of Technology in Austria. He is a graduate student of Prof. Mihyun Kang and is planning to stay with us until the end of August 2022.