论文标题
单体宽度：捕获等级宽度
Monoidal Width: Capturing Rank Width
论文作者
论文摘要
作者最近引入了单体宽度，以衡量分解形态在单体类别中的复杂性。我们已经表明，在图形的单层类别中，单宽宽度及其变体可用于捕获树宽度，路径宽度和分支宽度。在本文中，我们研究了一类矩阵中的单宽宽度，并扩展到不同的单型开放图类别，其中连通性信息用矩阵代数处理，并且图形沿边缘而不是顶点组成。我们表明，在这里，单宽宽度捕获了等级宽度：近年来受到很多关注的图形复杂度的度量。
Monoidal width was recently introduced by the authors as a measure of the complexity of decomposing morphisms in monoidal categories. We have shown that in a monoidal category of cospans of graphs, monoidal width and its variants can be used to capture tree width, path width and branch width. In this paper we study monoidal width in a category of matrices, and in an extension to a different monoidal category of open graphs, where the connectivity information is handled with matrix algebra and graphs are composed along edges instead of vertices. We show that here monoidal width captures rank width: a measure of graph complexity that has received much attention in recent years.
