On the boundary of the region defined by homomorphism densities
On the boundary of the region defined by homomorphism densities
复制标题
在同态密度定义的区域的边界上
作者：
Hamed Hatami;S. Norin
Kruskal-Katona定理与Razborov定理一起确定了有限图中由边和三角形的同态密度定义的点集的闭包。这个区域的边界是代数曲线的可数并，特别地，它几乎处处可微。我们可以更一般地考虑由一系列给定图的同态密度定义的区域，并询问边界是否像三角形和边的情况那样表现良好。为了回答这个问题的否定，我们构造的例子表明，限制的边界，某些超平面可以无处可微的部分。
The Kruskal-Katona theorem together with a theorem of Razborov determine the closure of the set of points defined by the homomorphism density of the edge and the triangle in finite graphs. The boundary of this region is a countable union of algebraic curves, and in particular, it is almost everywhere differentiable. One can more generally consider the region defined by the homomorphism densities of a list of given graphs, and ask whether the boundary is as well-behaved as in the case of the triangle and the edge. Towards answering this question in the negative, we construct examples which show that the restrictions of the boundary to certain hyperplanes can have nowhere differentiable parts.
有限强制图子和排列
DOI：
10.1016/j.jctb.2014.07.007
发表时间：
2015
期刊：
J. Comb. Theory, Ser. B
影响因子：
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作者：
R. Glebov;A. Grzesik;T. Klimošová;D. Král’
通讯作者：
D. Král’