Arborescences of Random Covering Graphs
Muchen Ju, Ni, Junjie, Kaixin Wang, Yihan Xiao · arXiv (Cornell University) · 2024
A rooted arborescence of a directed graph is a spanning tree directed towards a particular vertex. A recent work of Chepuri et al. showed that the arborescences of a covering graph of a directed graph G are closely related to the arborescences of G. In this paper, we study the weighted sum of arborescences of a random covering graph and give a formula for the expected value, resolving a conjecture of Chepuri et al.