arXiv subjects

P. P. Malavadkar

Publications and source records attributed to P. P. Malavadkar.

4 recordsLinked to original sources

arXiv2022

A note on connectivity preserving splitting operation for matroids representable over $GF(p)$

The splitting operation on a $p$-matroid does not necessarily preserve connectivity. It is observed that there exists a single element extension of the splitting matroid which is connected. In this paper, we define the element splitting operation on $p$-matroids which is a splitting operation followed by a single element extension. It is proved that element splitting operation on connected $p$-matroid yields a connected $p$-matroid. We give a sufficient condition to yield Eulerian $p$-matroids from Eulerian $p$-matroids under the element splitting operation. A sufficient condition to obtain hamiltonian $p$-matroid by applying element splitting operation on $p$-matroid is also provided.

math.CO↗

arXiv2018

A Forbidden-Minor Characterization for the Class of graphic Matroids which yield the Co-graphic Element-Splitting Matroids

The element splitting operation on a graphic matroid, in general may not yield a cographic matroid. In this paper, we give a necessary and sufficient condition for the graphic matroid to yield cographic matroid under the element splitting operation.

math.CO↗

arXiv2018

A note on connectivity of splitting matroids

Fleischner introduced the idea of splitting a vertex of degree at least three in a connected graph and used the operation to characterize Eulerian graphs. Raghunathan et. al. extended the splitting operation from graphs to binary matroids. It has been studied that splitting operation, in general, may not preserve the connectedness of the binary matroid. Interestingly, it is true that the splitting matroid of a disconnected matroid may be connected. In this paper, we characterize the binary disconnected matroids whose splitting matroid is connected.

math.CO↗

arXiv2016

The Closure Operator of es-Splitting Matroids

The es-splitting operation for binary matroids is a natural generalization of Slater's n-line splitting operation on graphs. In this paper, we characterize the closure operator of the es-splitting binary matroid $M^e_X$ in terms of the closure operator of the original binary matroid $M$. We also characterize the flats of the es-splitting binary matroid $M^e_X$ in terms of the flats of the original binary matroid $M$.

math.CO↗