Degree-balanced decompositions of cubic graphs
Combinatorics
2025-05-13 v2 Discrete Mathematics
Abstract
We show that every cubic graph on vertices contains a spanning subgraph in which the number of vertices of each degree deviates from by at most , 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.
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}
}