Uniform scrambles on graphs
Uniform scrambles on graphs
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发表时间：
2021-08
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通讯作者：
Lisa Cenek;L. Ferguson;Eyobel Gebre;Cassandra Marcussen;Jason Meintjes;Ralph Morrison;Liz Ostermeyer;Shefali Ramakrishna
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作者：
Lisa Cenek;L. Ferguson;Eyobel Gebre;Cassandra Marcussen;Jason Meintjes;Ralph Morrison;Liz Ostermeyer;Shefali Ramakrishna
连通重图上的scramble是连通子图的集合，它推广了bramble的概念。图的打乱数是最近发展起来的一个求图的最大打乱阶数的工具。我们目前的结果与一个固定数量的顶点的所有连通子图的混乱，使用这些来计算混乱数和角都为大家庭的图形，并为具体的例子，如$4$-和$5$-维超立方体图。我们还研究了扰码的切蛋数的计算复杂度。
A scramble on a connected multigraph is a collection of connected subgraphs that generalizes the notion of a bramble. The maximum order of a scramble, called the scramble number of a graph, was recently developed as a tool for lower bounding divisorial gonality. We present results on the scramble of all connected subgraphs with a fixed number of vertices, using these to calculate scramble number and gonality both for large families of graphs, and for specific examples like the $4$- and $5$-dimensional hypercube graphs. We also study the computational complexity of the egg-cut number of a scramble.