On $k$-Connected $\Gamma$-Extensions of Binary Matroids
- Resource Type
- Working Paper
- Authors
- Borse, Y. M.; Mundhe, Ganesh
- Source
- Subject
- Mathematics - Combinatorics
- Language
Slater introduced the point-addition operation on graphs to classify 4-connected graphs. The $\Gamma$-extension operation on binary matroids is a generalization of the point-addition operation. In this paper, we obtain necessary and sufficient conditions to preserve $k$-connectedness of a binary matroid under the $\Gamma$-extension operation. We also obtain a necessary and sufficient condition to get a connected matroid from a disconnected binary matroid using the $\Gamma$-extension operation.