TY  - JOUR
T1  - Generalization of pinching operation to binary matroids
AU  - Ghorbani, Vahid
AU  - Azadi, Ghodratollah
AU  - Azanchiler, Habib
PY  - 2020
DA  - September
DO  - 10.13069/jacodesmath.784992
JF  - Journal of Algebra Combinatorics Discrete Structures and Applications
PB  - iPeak Academy
WT  - DergiPark
SN  - 2148-838X
SP  - 247
EP  - 258
VL  - 7
IS  - 3
LA  - en
AB  - In this paper, we generalize the pinching operation on two edges of graphs to binarymatroids 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.
KW  - Binary matroid
KW  - Connectivity
KW  - Pinching
KW  - Splitting
KW  - Splitting off
KW  - Element splitting
CR  - [1] G. Azadi, Generalized splitting operation for binary matroids and related results, Ph.D. Thesis, University
of Pune, 2001.
CR  - [2] A. Frank, Edge–connection of graphs, digraphs, and hypergraphs, More Sets, Graphs and Numbers
15 (2006) 93–141.
CR  - [3] M. M. Shikare, K. V. Dalvi, S. B. Dhotre, Splitting off operation for binary matroids and its applications,
Graph and Combinatorics 27 (2011) 871–882.
CR  - [4] J. Oxley, Matroid Theory, Oxford University Press, 2nd ed. 2011.
CR  - [5] T. T. Raghunathan, M. M. Shikare, B. N. Waphare, Splitting in a binary matroid, Discrete Math.
184 (1998) 267–271.
CR  - [6] D. J. A. Welsh, Euler and bipartite matroids, Journal of Combinatorial Theory 6(4) (1969) 375–377.
CR  - [7] D. West, Introduction to graph theory, Prentice–Hall, 2nd ed. 2001.
UR  - https://doi.org/10.13069/jacodesmath.784992
L1  - https://dergipark.org.tr/en/download/article-file/1255615
ER  -