A characterization of 4-connected graphs with no 6-wheel minor

Zijun Chen; Yuqi Xu; Weihua Yang

A characterization of 4-connected graphs with no 6-wheel minor

Combinatorics 2026-05-15 v1

Authors: Zijun Chen , Yuqi Xu , Weihua Yang

Abstract

For each integer $n\geq 3$ , let $W_n$ denote the wheel graph obtained by connecting a single vertex to all vertices of a cycle of length $n$ . In particular, $W_6$ is obtained from the Petersen graph by contracting three edges incident with a common vertex. In this paper, we determine all $4$ -connected graphs that do not contain $W_6$ as a minor.

Keywords

wheel graph graph minor 4-connected graph Petersen graph graph characterization

Cite

@article{arxiv.2605.15039,
  title  = {A characterization of 4-connected graphs with no 6-wheel minor},
  author = {Zijun Chen and Yuqi Xu and Weihua Yang},
  journal= {arXiv preprint arXiv:2605.15039},
  year   = {2026}
}

Comments

15 pages, 8 figures

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