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

Key Points

• 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.