Year: 2026
Type: preprint
Abstract: It is shown that every Eulerian digraph on $n$ vertices with more than $(t-1)n$ arcs contains every oriented tree with $t$ edges. The digraphs have no loops or repeated arcs, but opposite arcs are permitted. The bound is sharp for each fixed oriented tree, as witnessed by disjoint unions of complete bidirected graphs. Previously, such tight bounds were not known, even just for directed paths. This can be considered as a directed analog of the recently proved Erdős-Sós conjecture. The result was proved by GPT-6 Astra.
Source: arXiv (Cornell University)
Authors: Mubayi, Dhruv, Verstraete, Jacques
Institution: University of California San Diego
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7212270109