论文标题
关于Eulerian $ es $ -splitting $ P $ -Matroids的表征
On the characterization of Eulerian $es$-splitting $p$-matroids
论文作者
论文摘要
二进制无桥的$ splitting操作从未产生欧拉的矩阵。但是，对于$ GF（P），（P> 2）的代表性的矩阵，$ p $ -Matroids，$ es $ splitting操作可能会产生Eulerian Matroids。在这项工作中，我们介绍了$ p $ -Matroids的$ es $ splitting操作，并在$ es $ splittit操作后表征了$ p $ - 莫托德的类别，从而产生欧拉型Matroids。分别讨论了电路的表征和由此产生的Matroid的基础，分别在电路和原始Matroid的基础方面进行了$ ES $分配操作的表征。我们还证明了$ p $ -Matroids上的$ es $ splitting操作可保留连接性和3个连接性。还提供了足够的条件，可以从$ es $ splitting操作下从hamiltonian $ p $ p $ matroid获取hamiltonian $ p $ -matroid。
The $es$-splitting operation on binary bridge-less matroids never produces an Eulerian matroid. But for matroids representable over $GF(p),(p>2),$ called $p$-matroids, the $es$-splitting operation may yield Eulerian matroids. In this work, we introduce the $es$-splitting operation for $p$-matroids and characterize a class of $p$-matroids yielding Eulerian matroids after the $es$-splitting operation. Characterization of circuits, and bases of the resulting matroid, after the $es$-splitting operation, in terms of circuits, and bases of the original matroid, respectively, are discussed. We also proved that the $es$-splitting operation on $p$-matroids preserves connectivity and 3-connectedness. Sufficient condition to obtain Hamiltonian $p$-matroid from Hamiltonian $p$-matroid under $es$-splitting operation is also provided.
