论文标题
图密度统治指数
The Graph Density Domination Exponent
论文作者
论文摘要
对于图形$ g $和$ h $，可以确定$ t（g，w）$和$ t（h，w）$的一般图$ W $之间的关系？我们通过密度统治指数的框架来研究此问题，该指数定义为最小的常数$ c $，因此每个图$ w $ $ t（g，w）\ ge t（h，w）^c $。这种广泛的概括涵盖了Sidorenko的猜想，Erdős-Simonover在路径上定理以及与图形同态密度有关的各种其他陈述。我们介绍了一些通用工具来估计密度支配指数，并将以前的结果扩展到新的图形制度。
For graphs $G$ and $H$, what relations can be determined between $t(G,W)$ and $t(H,W)$ for a general graph $W$? We study this problem through the framework of the density domination exponent, which is defined to be the smallest constant $c$ such that $t(G,W)\ge t(H,W)^c$ for every graph $W$. This broad generalization encompasses the Sidorenko conjecture, the Erdős-Simonovits Theorem on paths, and a variety of other statements relating graph homomorphism densities. We introduce some general tools for estimating the density domination exponent, and extend previous results to new graph regimes.
