Dmitry Rybin on X: "Dinitz-Garg-Goemans conjecture is false. This graph theory problem was open for ~30 years.

The graph below has fractional flow cost 58. Any unsplittable flow (with capacity violation <=15) has cost at least 60.

Chat with GPT 5.6 Pro where this was found: https://t.co/Oi2PQoab2h https://t.co/3ihncPMpve" / X<br>Post

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Dmitry Rybin<br>@DmitryRybin1

Dinitz-Garg-Goemans conjecture is false. This graph theory problem was open for ~30 years.

The graph below has fractional flow cost 58. Any unsplittable flow (with capacity violation chatgpt.com/share/6a60b2eb…

span:not(:empty)~span:not(:empty)]:before:content-['·'] [&>span:not(:empty)~span:not(:empty)]:before:px-1 [&>span:not(:empty)~span:not(:empty)]:before:shrink-0">12:18 PM · Jul 22, 20262.6MViews

1880188<br>6670667<br>7.6K07.6K<br>2.9K02.9K

span:not(:empty)~span:not(:empty)]:before:content-['·'] [&>span:not(:empty)~span:not(:empty)]:before:px-1 [&>span:not(:empty)~span:not(:empty)]:before:shrink-0 min-w-0 overflow-hidden">Dmitry Rybin<br>@DmitryRybin1

15h

I know counterexamples to old conjectures are becoming a meme at this point. But I really cared about this problem and spent many weeks thinking about it a while ago (in both directions, proof and disproof).

I think almost all graph flows experts thought about this problem.

12012<br>11011<br>1.5K01.5K<br>svg]:size-5 text-body hover:bg-mix-current hover:bg-mix-amount-10 active:bg-mix-current active:bg-mix-amount-15 focus-visible:bg-mix-current focus-visible:bg-mix-amount-10 outline-current -m-2 shrink-0 cursor-pointer border-transparent p-0 text-body size-9 [&>svg]:size-[1.25em] [&>[data-engagement-icon]]:size-[1.25em] group-hover:bg-mix-current group-hover:bg-mix-amount-10" aria-label="View count" type="button" data-state="closed" href="/DmitryRybin1/status/2079906232069177643/quotes">108K0108K

span:not(:empty)~span:not(:empty)]:before:content-['·'] [&>span:not(:empty)~span:not(:empty)]:before:px-1 [&>span:not(:empty)~span:not(:empty)]:before:shrink-0 min-w-0 overflow-hidden">Dmitry Rybin<br>@DmitryRybin1

15h

The conjecture was based on absolutely stunning result of Dinitz, Garg, and Goemans: any fractional flow can be routed to unsplittable flow by violating graph capacities by at most max(demand).

The chat with gpt pro here is an absolute meme

202<br>505<br>8740874<br>svg]:size-5 text-body hover:bg-mix-current hover:bg-mix-amount-10 active:bg-mix-current active:bg-mix-amount-15 focus-visible:bg-mix-current focus-visible:bg-mix-amount-10 outline-current -m-2 shrink-0 cursor-pointer border-transparent p-0 text-body size-9 [&>svg]:size-[1.25em] [&>[data-engagement-icon]]:size-[1.25em] group-hover:bg-mix-current group-hover:bg-mix-amount-10" aria-label="View count" type="button" data-state="closed" href="/DmitryRybin1/status/2079907499545919968/quotes">95K095K

span:not(:empty)~span:not(:empty)]:before:content-['·'] [&>span:not(:empty)~span:not(:empty)]:before:px-1 [&>span:not(:empty)~span:not(:empty)]:before:shrink-0 min-w-0 overflow-hidden">Francisco Costa 🇵🇹

@phelgo

12h

The future of Science, ladies and gentlemen.

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Relevant people<br>Dmitry Rybin@DmitryRybin1Follow<br>Cofounder $100M AI Startup in Shenzhen, Algorithm Discovery + Math (we’re hiring) | ML PhD CUHK, BSc. Math HSE | IMC🥇National Math Olympiad🥇

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