For an edge $uv$ of a finite simple graph $G$, its imbalance is $|d_G(u)-d_G(v)|$, and the imbalance multiset $M_G$ consists of the imbalances of all edges of $G$. Kozerenko and Skochko conjectured that $M_G$ is graphic whenever every edge has positive imbalance. We prove this conjecture. The main ingredient is a lower bound for the truncated sum $\sum_{e\in E(G)}\min\{k,\operatorname{imb}_G(e)\}$ when at least $k$ edges have imbalance at least $k$. This bound yields all Erdos-Gallai inequalities for the nonincreasing list of edge imbalances; a parity computation then completes the proof.

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