A constructive characterization of uniformly 4-connected graphs

Xiang Chen; Shuai Kou; Chengfu Qin; Liqiong Xu; Weihua Yang

A constructive characterization of uniformly 4-connected graphs

Combinatorics 2025-07-11 v1

Authors: Xiang Chen , Shuai Kou , Chengfu Qin , Liqiong Xu , Weihua Yang

Abstract

A constructive characterization of the class of uniformly $4$ -connected graphs is presented. The characterization is based on the application of graph operations to appropriate vertex and edge sets in uniformly $4$ -connected graphs, that is, any uniformly $4$ -connected graph can be obtained from $C_5^2$ or $C_6^2$ by a number of $\Delta_1^+$ or $\Delta_2^+$ -operations to quasi $4$ -compatible sets.

Keywords

graph theory graph connectivity graph theory of groups

Cite

@article{arxiv.2507.07656,
  title  = {A constructive characterization of uniformly 4-connected graphs},
  author = {Xiang Chen and Shuai Kou and Chengfu Qin and Liqiong Xu and Weihua Yang},
  journal= {arXiv preprint arXiv:2507.07656},
  year   = {2025}
}

A constructive characterization of uniformly 4-connected graphs

Abstract

Keywords

Cite

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