August 21, 2025The Electronic Journal of CombinatoricsOpen Access

A Characterization of $4$-Connected Graphs with no K3,3+v-Minor

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All 4-connected graphs lacking a K_{3,3}+v minor are characterized clearly, offering a comprehensive understanding of their structure.
The identification of K_{3,3}+v minors helps in analyzing graph connectivity in theoretical frameworks or applications.
Analysis employed structural methods, focusing on how vertices and cycles interact without forming specific minors.
Implications suggest potential avenues for further research in graph theory and combinatorial structures.

Implication

This analysis identifies 4-connected graphs without K_{3,3}+v minors, suggesting structural insights into graph properties.

Abstract

Let K3,3+v be the graph obtained by adding a new vertex v to K3,3 and joining v to the four vertices of a $ 4 $-cycle. In this paper, we characterize all $ 4 $-connected graphs that do not contain K3,3+v as a minor.

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Cite This Study

Wei et al. (2025) studied this question.

synapsesocial.com/papers/68af5228ad7bf08b1eada3e5 https://doi.org/10.37236/13051

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Implication

This analysis identifies 4-connected graphs without K_{3,3}+v minors, suggesting structural insights into graph properties.

A Characterization of $4$-Connected Graphs with no K3,3+v-Minor

Key Points

Implication

Abstract

Discussion

Cite This Study

A Characterization of $4$-Connected Graphs with no K3,3+v-Minor

Key Points

Implication

Abstract

Discussion

Cite This Study

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