A note on connectivity preserving splitting operation for matroids representable over $GF(p)$
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866909685346467840 |
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| author | Malavadkar, P. P. Gunjal, Sachin Jagadale, Uday |
| author_facet | Malavadkar, P. P. Gunjal, Sachin Jagadale, Uday |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2003_03617 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A note on connectivity preserving splitting operation for matroids representable over $GF(p)$ Malavadkar, P. P. Gunjal, Sachin Jagadale, Uday Combinatorics 05B35, 05C50, 05C83 G.2 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. |
| title | A note on connectivity preserving splitting operation for matroids representable over $GF(p)$ |
| topic | Combinatorics 05B35, 05C50, 05C83 G.2 |
| url | https://arxiv.org/abs/2003.03617 |