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arXiv · 2107.11138

Weak saturation stability

Olga Kalinichenko·Maksim Zhukovskii
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Abstract

The paper studies wsat$(G,H)$ which is the minimum number of edges in a weakly $H$-saturated subgraph of $G$. We prove that wsat$(K_n,H)$ is `stable' - remains the same after independent removal of every edge of $K_n$ with constant probability - for all pattern graphs $H$ such that there exists a `local' set of edges percolating in $K_n$. This is true, for example, for cliques and complete bipartite graphs. We also find a threshold probability for the weak $K_{1,t}$-saturation stability.

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Olga Kalinichenko, Maksim Zhukovskii. 2022-07-29. Weak saturation stability. https://arxiv.org/abs/2107.11138

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