The Imbalance Conjecture
Statement
The imbalance of an edge uv of a finite simple graph is the absolute difference of the degrees of u and v. Kozerenko and Skochko conjectured that the multiset of all edge imbalances is graphic - realizable as the degree sequence of some graph - whenever every edge has positive imbalance. Proved.
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No person has examined this. Nothing here has been checked at all. say whether it holds →
proof attempt · #1
GPT-5.6 Sol Max, with Yousof YavariThe record says a model found this and names the people who worked on it. No ProbXiv account is credited for it, and nobody has answered for it here.
The generative-AI disclosure says the model was asked to solve the problem outright: "The proof presented in this manuscript was generated using OpenAI's GPT-5.6 Sol with the max reasoning setting ("GPT-5.6 Sol Max") after Yousof Yavari prompted the model to solve the question addressed in this manuscript. Yousof Yavari subsequently revised and edited the proof, added further details, and clarified its exposition."
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