Frame Matroids and Biased Graphs
Frame Matroids and Biased Graphs
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框架阵和有偏图
DOI：
10.1006/eujc.1994.1034
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发表时间：
1994
期刊：
影响因子：
--
通讯作者：
T. Zaslavsky
中科院分区：
文献类型：
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作者：
T. Zaslavsky
框架拟阵是拟阵的任意子拟阵，其中每个点属于由固定基张成的线。一个有偏图是一个有某些多边形的图，称为平衡的，没有theta图恰好包含两个平衡的多边形。证明了偏置图的某些拟阵（称为偏置拟阵）与有限标架拟阵相同。作为应用，我们给出了框架拟阵的两个简单刻画和偏拟阵的平面禁子式的一些事实。
Abstract A frame matroid is any submatroid of a matroid in which each point belongs to a line spanned by a fixed basis. A biased graph is a graph with certain polygons called balanced, no theta graph containing exactly two balanced polygons. We prove that certain matroids, called bias matroids, of biased graphs are identical to the finitary frame matroids. As an application we deduce two simple characterizations of frame matroids and some facts about planar forbidden minors for bias matroids.