Dmitry Rybin on X: "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." / X<br>Post

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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

Jul 22

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…

252<br>882<br>9.4K<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/2079904005652893709/quotes">4.1M

Dmitry Rybin<br>@DmitryRybin1

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.<br>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">12:27 PM · Jul 22, 2026151.9KViews

15<br>15<br>1.9K<br>56

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

Jul 22

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

1.1K<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">131K

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">Verdi Erel Ergün 🇺🇸<br>@vergun

Jul 22

Your 'many weeks thinking about it' was asking the model to try again 4x. 😂

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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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