Suppose you take a graph G (a collection of nodes joined by edges), make an exact copy of it, G', and join G and G' with edges along some of their corresponding vertices.
If you randomly delete edges from G and G' with the same probability (but don't delete any of the edges you added between G and G'), can it ever be *less likely* that you can still get from a vertex x in graph G to another vertex y also in G than it is to get from x to the copy of y in G'?
The conjecture that no choice of G can make it less likely is known as the Bunkbed Conjecture. And three mathematicians have just found a counterexample!
H/T Timothy Gowers, Javier Campos
https://igorpak.wordpress.com/2024/10/01/the-bunkbed-
conjecture-is-false/
https://arxiv.org/abs/2410.02545
Greg Egan /
npub12c…gd38p
2024-10-04 10:16:47
Author Public Key
npub12cuzzqzv8e8y7na77a9zv47mx2v6pec60qs5h7takzmv5p0mw0fsmgd38pPublished at
2024-10-04 10:16:47Event JSON
{
"id": "48961addcbb3e95ba74f63a6beaba1a69fdd8ea8ffd7e6dc6063eb0175f5054b",
"pubkey": "563821004c3e4e4f4fbef74a2657db3299a0e71a78214bf97db0b6ca05fb73d3",
"created_at": 1728037007,
"kind": 1,
"tags": [
[
"proxy",
"https://mathstodon.xyz/@gregeganSF/113248633341083964",
"web"
],
[
"proxy",
"https://mathstodon.xyz/users/gregeganSF/statuses/113248633341083964",
"activitypub"
],
[
"L",
"pink.momostr"
],
[
"l",
"pink.momostr.activitypub:https://mathstodon.xyz/users/gregeganSF/statuses/113248633341083964",
"pink.momostr"
],
[
"-"
]
],
"content": "Suppose you take a graph G (a collection of nodes joined by edges), make an exact copy of it, G', and join G and G' with edges along some of their corresponding vertices.\n\nIf you randomly delete edges from G and G' with the same probability (but don't delete any of the edges you added between G and G'), can it ever be *less likely* that you can still get from a vertex x in graph G to another vertex y also in G than it is to get from x to the copy of y in G'?\n\nThe conjecture that no choice of G can make it less likely is known as the Bunkbed Conjecture. And three mathematicians have just found a counterexample!\n\nH/T Timothy Gowers, Javier Campos\n\nhttps://igorpak.wordpress.com/2024/10/01/the-bunkbed-\nconjecture-is-false/\n\nhttps://arxiv.org/abs/2410.02545",
"sig": "3736a9cc0d2e934947d4f5264401c32adf00c05727cd175f3f67aff2385c5b099b85f4bde9c7a305d49f434124f04d7fedc7b6c3f4ae19e8441c610ad67344b8"
}