Generalization of pinching operation to binary matroids

Year 2020, Volume: 7 Issue: 3, 247 - 258, 06.09.2020

Vahid Ghorbani , Ghodratollah Azadi Habib Azanchiler

https://doi.org/10.13069/jacodesmath.784992

https://izlik.org/JA88NY94NY

Abstract

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.

Keywords

Binary matroid , Connectivity , Pinching , Splitting , Splitting off , Element splitting

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