当前位置: X-MOL 学术Random Struct. Algorithms › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
On the inducibility problem for random Cayley graphs of abelian groups with a few deleted vertices
Random Structures and Algorithms ( IF 1 ) Pub Date : 2021-04-23 , DOI: 10.1002/rsa.21010
Jacob Fox 1 , Lisa Sauermann 1 , Fan Wei 1
Affiliation  

Given a k-vertex graph H and an integer n, what are the n-vertex graphs with the maximum number of induced copies of H? This question is closely related to the inducibility problem introduced by Pippenger and Golumbic in 1975, which asks for the maximum possible fraction of k-vertex subsets of an n-vertex graph that induce a copy of H. Huang, Lee, and the first author proved that for a random k-vertex graph H, almost surely the n-vertex graphs maximizing the number of induced copies of H are the balanced iterated blow-ups of H. In this article, we consider the case where the graph H is obtained by deleting a small number of vertices from a random Cayley graph urn:x-wiley:rsa:media:rsa21010:rsa21010-math-0001 of an abelian group. We prove that in this case, almost surely all n-vertex graphs maximizing the number of induced copies of H are balanced iterated blow-ups of urn:x-wiley:rsa:media:rsa21010:rsa21010-math-0002.

中文翻译:

关于具有少量删除顶点的阿贝尔群的随机凯莱图的可归纳性问题

给定一个k顶点图H和一个整数n,具有H的最大诱导副本数的n顶点图是什么?这个问题与 Pippenger 和 Golumbic 在 1975 年引入的可归纳性问题密切相关,该问题要求引起H的副本的n顶点图的k顶点子集的最大可能分数。Huang、Lee 和第一作者证明,对于随机k顶点图H,几乎可以肯定使H的诱导副本数量最大化的n顶点图是H . 在本文中,我们考虑从一个阿贝尔群的随机凯莱图中删除少量顶点得到图H的情况urn:x-wiley:rsa:media:rsa21010:rsa21010-math-0001。我们证明,在这种情况下,几乎可以肯定所有使H的诱导副本数量最大化的n顶点图都是 的平衡迭代爆炸。urn:x-wiley:rsa:media:rsa21010:rsa21010-math-0002
更新日期:2021-04-23
down
wechat
bug