论文标题
关于在$ gf（P）$上表示的连通性保留分裂操作的连接说明
A note on connectivity preserving splitting operation for matroids representable over $GF(p)$
论文作者
论文摘要
$ P $ -Matroid上的分裂操作并不一定保留连接性。观察到存在连接的分裂曲线的单个元素扩展。在本文中，我们在$ p $ -Matroids上定义了元素分裂操作，这是一个分裂操作，然后是单个元素扩展。事实证明，连接的$ p $ -matroid上的元素拆分操作会产生连接的$ p $ -matroid。我们提供了足够的条件，可以在元素分割操作下从Eulerian $ P $ -Matroids产生Eulerian $ P $ -MATROID。还提供了足够的条件，可以通过在$ p $ -matroid上应用元素分裂操作来获取hamiltonian $ p $ -matroid。
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.
