combinatorics / Graph theory

The Imbalance Conjecture

The key step is a lower bound on the truncated imbalance sum, which yields every Erdos-Gallai inequality for the sorted imbalance list; a parity computation finishes it.

10Significance / 100
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combinatoricsAug 10, 2026Significance 10/100Registry: unreviewed

The Imbalance Conjecture

Prior state unknown→proved

The key step is a lower bound on the truncated imbalance sum, which yields every Erdos-Gallai inequality for the sorted imbalance list; a parity computation finishes it.

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The key step is a lower bound on the truncated imbalance sum, which yields every Erdos-Gallai inequality for the sorted imbalance list; a parity computation finishes it.

The key step is a lower bound on the truncated imbalance sum, which yields every Erdos-Gallai inequality for the sorted imbalance list; a parity computation finishes it.

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The Imbalance Conjecture — Mathematical Frontier Network