John D. Cook 8/18/2026

The imbalance theorem

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This article reports that the imbalance conjecture in graph theory has been proven by James Alexander Schreib and Yousof Yavari. The conjecture states that for any graph where no edge connects vertices of equal degree, the multiset of absolute degree differences across edges can be realized as the degree sequence of another graph. The article explains the theorem with an example and links to related graph theory posts.

The imbalance theorem

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