English

Degree-balanced decompositions of cubic graphs

Combinatorics 2025-05-13 v2 Discrete Mathematics

Abstract

We show that every cubic graph on nn vertices contains a spanning subgraph in which the number of vertices of each degree deviates from n4\frac{n}{4} by at most 12\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.

Keywords

Cite

@article{arxiv.2408.16121,
  title  = {Degree-balanced decompositions of cubic graphs},
  author = {Borut Lužar and Jakub Przybyło and Roman Soták},
  journal= {arXiv preprint arXiv:2408.16121},
  year   = {2025}
}
R2 v1 2026-06-28T18:27:04.450Z