Generalization of pinching operation to binary matroids
Vahid Ghorbani, Ghodratollah Azadi, Habib Azanchiler · Journal of Algebra Combinatorics Discrete Structures and Applications · 2020
In this paper, we generalize the pinching operation on two edges of graphs to binary matroids and investigate some of its basic properties. For $n\geq 2$, the matroid that is obtained from an $n$-connected matroid by this operation is a $k$-connected matroid with $k\in\{2,3,4\}$ or is a disconnected matroid. We find conditions to guarantee this $k$. Moreover, we show that Eulerian binary matroids are characterized by this operation and we also provide some interesting applications of this operation. Received: 14 April 2020 | Accepted: 1 May 2020