A Characterization of $4$-Connected Graphs with no $ K_{3,3}+v $-Minor

Let $ K_{3,3}+v $ be the graph obtained by adding a new vertex $ v $ to $ K_{3,3} $ and joining $ v $ to the four vertices of a $ 4 $-cycle. In this paper, we characterize all $ 4 $-connected graphs that do not contain $ K_{3,3}+v $ as a minor.

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Bibliographic Details
Published in	The Electronic journal of combinatorics Vol. 32; no. 3
Main Authors	Wei, Linsong, Xu, Yuqi, Yang, Weihua, Zhang, Yunxia
Format	Journal Article
Language	English
Published	22.08.2025
Online Access	Get full text

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Summary:	Let $ K_{3,3}+v $ be the graph obtained by adding a new vertex $ v $ to $ K_{3,3} $ and joining $ v $ to the four vertices of a $ 4 $-cycle. In this paper, we characterize all $ 4 $-connected graphs that do not contain $ K_{3,3}+v $ as a minor.
ISSN:	1077-8926 1077-8926
DOI:	10.37236/13051