图同态的二部交换技巧
The Bipartite Swapping Trick on Graph Homomorphisms
摘要：
本文给出了从$G$到$H$的图同态数的一个上界，其中$H$是一个具有某些性质的固定图，并且$G$在所有$N$ -顶点图，$d$ -正则图上都是变化的.这一结果推广了最近解决的猜想阿隆和卡恩的独立集的数量。Galvin和Tetali研究了当$H$是二分图时，从$G$到$H$的图同态的个数.我们也将我们的技术应用于图着色和独立集多面体。
英文摘要：
We provide an upper bound to the number of graph homomorphisms from $G$ to $H$, where $H$ is a fixed graph with certain properties, and $G$ varies over all $N$-vertex, $d$-regular graphs. This result generalizes a recently resolved conjecture of Alon and Kahn on the number of independent sets. We build on the work of Galvin and Tetali, who studied the number of graph homomorphisms from $G$ to $H$ when $H$ is bipartite. We also apply our techniques to graph colorings and stable set polytopes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
