We study a problem on edge percolation on product graphs G×K2. Here G is any finite graph and K2 consists of two vertices {0, 1} connected by an edge. Every edge in G × K2 is present with probability p independent of other edges. The Bunkbed conjecture states that for all G and p the probability that (u, 0) is in the same component as (v, 0) is greater than or equal to the probability that (u, 0) is in the same component as (v, 1) for every pair of vertices u, v ∈ G. We generalize this… CONTINUE READING