If M is a loopless matroid in which M/vbX and M/vbY are connected and X∩Y is non-empty, then one easily shows that M/vb(X∪Y) is connected. Likewise, it is straightforward to show that if G and H are n-connected graphs having at least n common vertices, then G ∪ H is n-connected. The purpose of this note is to prove a matroid connectivity result that is a common generalization of these two observations. © 1995.
Publication Source (Journal or Book title)
Oxley, J., & Wu, H. (1995). On matroid connectivity. Discrete Mathematics, 146 (1-3), 321-324. https://doi.org/10.1016/0012-365X(94)00179-2