Year: 2026
Type: preprint
Abstract: In the 1960s, Erdős 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 Hajós' conjecture up to a constant factor.
Source: arXiv (Cornell University)
Author: Kim, Jaehoon
Institution: Korea Advanced Institute of Science and Technology
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1474807751, G3812690899, G6572798828
OpenAlex ID: W7221055617