Year: 2026
Type: preprint
Abstract: In this paper, we study the extremal number of arborescences over orientations of a fixed graph. We prove that every alternating orientation of a plane Eulerian multigraph minimizes the rooted arborescence count among its Eulerian orientations. We also prove that every tournament of odd order maximizing the total number of arborescences is regular, and hence Eulerian. These results resolve Conjectures 5.1 and 5.4 of Bandekar et al. We further establish upper bounds for arborescence counts in orientations of complete bipartite graphs and characterize the orientations attaining them.
Source: arXiv (Cornell University)
Authors: Liu, Jianing, Xu, Zhijun
Institution: Nankai University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Award: G1224553440
OpenAlex ID: W7223006044