English

On $k$-Connected $\Gamma$-Extensions of Binary Matroids

Combinatorics 2018-12-05 v1

Abstract

Slater introduced the point-addition operation on graphs to classify 4-connected graphs. The Γ\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 kk-connectedness of a binary matroid under the Γ\Gamma-extension operation. We also obtain a necessary and sufficient condition to get a connected matroid from a disconnected binary matroid using the Γ\Gamma-extension operation.

Keywords

Cite

@article{arxiv.1812.01256,
  title  = {On $k$-Connected $\Gamma$-Extensions of Binary Matroids},
  author = {Y. M. Borse and Ganesh Mundhe},
  journal= {arXiv preprint arXiv:1812.01256},
  year   = {2018}
}
R2 v1 2026-06-23T06:30:38.660Z