Generalization of pinching operation to binary matroids

Yıl 2020, Cilt: 7 Sayı: 3, 247 - 258, 06.09.2020

Vahid Ghorbani , Ghodratollah Azadi Habib Azanchiler

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

Öz

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.

Anahtar Kelimeler

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

Kaynakça

• [1] G. Azadi, Generalized splitting operation for binary matroids and related results, Ph.D. Thesis, University of Pune, 2001.
• [2] A. Frank, Edge–connection of graphs, digraphs, and hypergraphs, More Sets, Graphs and Numbers 15 (2006) 93–141.
• [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.
• [4] J. Oxley, Matroid Theory, Oxford University Press, 2nd ed. 2011.
• [5] T. T. Raghunathan, M. M. Shikare, B. N. Waphare, Splitting in a binary matroid, Discrete Math. 184 (1998) 267–271.
• [6] D. J. A. Welsh, Euler and bipartite matroids, Journal of Combinatorial Theory 6(4) (1969) 375–377.
• [7] D. West, Introduction to graph theory, Prentice–Hall, 2nd ed. 2001.