An excluded minor theorem for the 6-wheel

Zijun Chen; Yuqi Xu; Weihua Yang

paper

An excluded minor theorem for the 6-wheel

arXiv:2605.15125

Abstract

For each integer $n \geq 3$ , the wheel graph $W_{n}$ is defined as the graph obtained by connecting a single vertex to all vertices of a cycle of length $n$ . In particular, $W_{6}$ can be uniquely obtained from the Petersen graph by contracting three edges incident to a common vertex. Gubser provided a characterization of all 3-connected planar $W_{6}$ -minor-free graphs. In this paper, we complete the characterization of $W_{6}$ -minor-free graphs by determining the 3-connected nonplanar cases.

34 pages, 20 figures