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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.
There has been substantial interest in estimating the value of a graph parameter, i.e., of a real-valued function defined on the set of finite graphs, by querying a randomly sampled substructure whose size is independent of the size of the input. Gra
We study the dynamics of coupled systems, ranging from maps supporting chaotic attractors to nonlinear differential equations yielding limit cycles, under different coupling classes, connectivity ranges and initial states. Our focus is the robustness
An edge-ordered graph is a graph with a total ordering of its edges. A path $P=v_1v_2ldots v_k$ in an edge-ordered graph is called increasing if $(v_iv_{i+1}) > (v_{i+1}v_{i+2})$ for all $i = 1,ldots,k-2$; it is called decreasing if $(v_iv_{i+1}) < (
We consider a data corruption scenario in the classical $k$ Nearest Neighbors ($k$-NN) algorithm, that is, the testing data are randomly perturbed. Under such a scenario, the impact of corruption level on the asymptotic regret is carefully characteri
We investigate the problem of determining how many monochromatic trees are necessary to cover the vertices of an edge-coloured random graph. More precisely, we show that for $pgg n^{-1/6}{(ln n)}^{1/6}$, in any $3$-edge-colouring of the random graph