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arXiv · 1604.08439

A proof of the bunkbed conjecture for the complete graph at $p=\frac{1}{2}$

Paul de Buyer
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Abstract

The bunkbed of a graph $G$ is the graph $G\times K_2 $. It has been conjectured that in the independent bond percolation model, the probability for $\left(u,0\right)$ to be connected with $\left(v,0\right)$ is greater than the probability for $\left(u,0\right)$ to be connected with $\left(v,1\right)$, for any vertex $u$, $v$ of $G$. In this article, we prove this conjecture for the complete graph in the case of the independent bond percolation of parameter $p=1/2$.

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Paul de Buyer. 2016-04-28. A proof of the bunkbed conjecture for the complete graph at $p=\frac{1}{2}$. https://arxiv.org/abs/1604.08439

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