论文标题
订购矩形的电路
Ordering Circuits of Matroids
论文作者
论文摘要
图的循环对其边缘集进行了自然的循环顺序，并且这些顺序是一致的，因为当且仅当它们在它们一起出现的每个循环中都相邻时，两个边缘在一个循环中相邻。订购的Matroid是其一组电路承认订购如此一致的人。在本文中，我们考虑了确定哪些矩形有序的问题。尽管我们能够为非二进制矩阵回答这个问题，但对于二进制矩阵仍然开放。我们举例说明了总体上对这个问题的潜在困难的见解。我们还表明，通过要求订购在每个Theta-graph限制二进制Matroid $ m $中保留三个弧线，我们保证$ m $在且仅当$ m $是图形时才订购。
The cycles of a graph give a natural cyclic ordering to their edge-sets, and these orderings are consistent in that two edges are adjacent in one cycle if and only if they are adjacent in every cycle in which they appear together. An orderable matroid is one whose set of circuits admits such a consistent ordering. In this paper, we consider the question of determining which matroids are orderable. Although we are able to answer this question for non-binary matroids, it remains open for binary matroids. We give examples to provide insight into the potential difficulty of this question in general. We also show that, by requiring that the ordering preserves the three arcs in every theta-graph restriction of a binary matroid $M$, we guarantee that $M$ is orderable if and only if $M$ is graphic.
