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- W3010584070 abstract "The element splitting operation on binary matroids due to Shikare, is a natural generalization of Slater's {it n-point splitting operation} on graphs. The present paper generalizes the notion of {it n-point splitting operation} on graphs to matroids representable over $GF(p)$. This operation on a given matroid representable over $GF(p)$ yields a matroid representable over $GF(p)$. We characterize circuits, bases and hyperplanes of the resulting matroid in terms of the circuits, bases and hyperplanes of the original matroid $M$, respectively. We also explore the effect of this operation on Eulerian, bipartite and connected matroids which are representable over $GF(p)$. This operation, in general, may not preserve the connectedness of the given matroid. We provide a necessary and sufficient condition for a connected matroid representable over $GF(p)$ to yield a connected matroid representable over $GF(p)$ by the element splitting operation." @default.
- W3010584070 created "2020-03-13" @default.
- W3010584070 creator A5013819929 @default.
- W3010584070 date "2020-03-07" @default.
- W3010584070 modified "2023-09-27" @default.
- W3010584070 title "Element splitting operation for matroids representable over $GF(p)$" @default.
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