Degree-balanced decompositions of cubic graphs
<|reference_start|>Degree-balanced decompositions of cubic graphs: We show that every cubic graph on $n$ vertices contains a spanning subgraph in which the number of vertices of each degree deviates from $\frac{n}{4}$ by at most $\frac{1}{2}$, up to three exceptions. This resolves the conjecture of Alon and Wei (Irregular subgraphs, Combin. Probab. Comput. 32(2) (2023), 269--283) for cubic graphs.<|reference_end|>
@article{lužar2024degree-balanced,
    title={Degree-balanced decompositions of cubic graphs},
    author={Borut Luv{z}ar and Jakub Przyby{l}o and Roman Sot'ak},
    journal={arXiv preprint arXiv:2408.16121},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.16121},
    primaryClass={math.CO cs.DM}
}