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arXiv · 2012.02050

A General Dependency Structure for Random Graphs and Its Effect on Monotone Properties

Zohre Ranjbar-Mojaveri·Andras Farago
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Abstract

We consider random graphs in which the edges are allowed to be dependent. In our model the edge dependence is quite general, we call it $p$-robust random graph. It means that every edge is present with probability at least $p$, regardless of the presence/absence of other edges. This is more general than independent edges with probability $p$, as we illustrate with examples. Our main result is that for any monotone graph property, the $p$-robust random graph has at least as high probability to have the property as an Erdos-Renyi random graph with edge probability $p$. This is very useful, as it allows the adaptation of many results from classical Erdos-Renyi random graphs to a non-independent setting, as lower bounds.

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Zohre Ranjbar-Mojaveri, Andras Farago. 2020-12-03. A General Dependency Structure for Random Graphs and Its Effect on Monotone Properties. https://arxiv.org/abs/2012.02050

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