Jaehoon Kim

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Preprint Oct 2026

A proof of the Erd\H{o}s-Gallai cycle decomposition conjecture

In the 1960s, Erd\H{o}s and Gallai conjectured that the edges of every $n$-vertex graph can be decomposed into $O(n)$ cycles and edges. We prove this conjecture. Equivalently, every Eulerian graph on $n$ vertices can be decomposed into $O(n)$ cycles, which confirms Haj\'os'conjecture up to a constant factor.

Jaehoon Kim · 0 citations

Preprint Oct 2026

A proof of the Erd\H{o}s--Gallai cycle decomposition conjecture

In the 1960s, Erd\H{o}s and Gallai conjectured that the edges of every $n$-vertex graph can be decomposed into $O(n)$ cycles and edges. We prove this conjecture. Equivalently, every Eulerian graph on $n$ vertices can be decomposed into $O(n)$ cycles, which confirms Haj\'os'conjecture up to a constant factor.

Jaehoon Kim · 0 citations

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