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Dong Yeap Kang (강동엽), Fragile minor-monotone parameters under random edge perturbation
Tuesday, February 18, 2020 @ 4:30 PM - 5:30 PM KST
We investigate how minor-monotone graph parameters change if we add a few random edges to a connected graph $H$. Surprisingly, after adding a few random edges, its treewidth, treedepth, genus, and the size of a largest complete minor become very large regardless of the shape of $H$. Our results are close to best possible for various cases. We also discuss analogous results for randomly perturbed bipartite graphs as well as the size of a largest complete odd minor in randomly perturbed graphs.