English

Equating three degrees of graphs

Combinatorics 2025-05-02 v1

Abstract

In this paper, we prove that, for every graph with at least 5 vertices, one can delete at most 3 vertices such that the subgraph obtained has at least three vertices with the same degree. This solves an open problem of Caro, Shapira and Yuster [Electron. J. Combin. 21 (2014) P1.24].

Keywords

Cite

@article{arxiv.2505.00504,
  title  = {Equating three degrees of graphs},
  author = {Zhen Liu and Qinghou Zeng},
  journal= {arXiv preprint arXiv:2505.00504},
  year   = {2025}
}
R2 v1 2026-06-28T23:17:58.330Z