Prohibited Minors For Graphic Matroids That Gives A Binary Gammoid After Splitting

2023/10/05 by S. D. Solanki, Solanki, S. D., S. B. Dhotre +1
Computer Science · #Advanced Algebra and Logic #Constraint Satisfaction and Optimization

paper · pdf · doi:10.48550/arxiv.2310.03490

Abstract

Splitting operation in Matroid Theory does not preserve graphicness, connectedness, cographicness, etc. Also, the splitting of binary gammoid does not necessarily be binary gammoid after splitting. We have characterized a class of graphic matroids that gives binary gammoids after splitting. We have obtained prohibited minors for graphic and cographic matroid which gives binary gammoid after splitting using two and three elements.

Related

• Forbidden Minor Characterization of 3-Fold-3-Splitting of Binary Gammoid
• A Forbidden-Minor Characterization for the Class of graphic Matroids which yield the Co-graphic Element-Splitting Matroids
• On graphic splitting of regular matroids
• On graphic elementary lifts of graphic matroids
• Elementary Lift and Single Element Coextension of A Binary Gammoid