## Random graph matching at Otter's tree-counting threshold via counting chandeliers

Given a pair of graphs, the problem of graph matching or network alignment refers to finding the underlying vertex correspondence that maximally aligns the edges. This is a ubiquitous problem arising in a variety of applications across diverse fields such as network privacy, computational biology, computer vision, and natural language processing. Graph matching is an instance of the notoriously difficult quadratic assignment problem (QAP), which is NP-hard to solve or approximate.