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Tuan Anh Do, Rank- and tree-width of supercritical random graphs

Monday, March 14, 2022 @ 4:30 PM - 5:30 PM KST

Room B232, IBS (기초과학연구원)


Tuan Anh Do (Tuấn Anh Đỗ)
Graz University of Technology / IBS Discrete Mathematics Group

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.


Monday, March 14, 2022
4:30 PM - 5:30 PM KST
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Room B232
IBS (기초과학연구원)


Sang-il Oum (엄상일)
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IBS 이산수학그룹 Discrete Mathematics Group
기초과학연구원 수리및계산과학연구단 이산수학그룹
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IBS Discrete Mathematics Group (DIMAG)
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