A Proof of the Bunkbed Conjecture for the Complete Graph at p=1/2

Paul de Buyer (1)

1 UPN - Université Paris Nanterre

The bunkbed of a graph G is the graph G × {0, 1}. It has been conjectured that in the independent bond percolation model, the probability for (u, 0) to be connected with (v, 0) is greater than the probability for (u, 0) to be connected with (v, 1), 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.

Domaines: Combinatoire [math.CO]; Probabilités [math.PR]

Paul de Buyer. A Proof of the Bunkbed Conjecture for the Complete Graph at p=1/2. 2018. ⟨hal-01706589⟩