2024/10/03 by Florian Reich, Reich, Florian
Computer Science · #05C20 #05C63 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems
paper · pdf · doi:10.48550/arxiv.2410.02624
openalex publication_date 2024/10/03 · openalex created_date 2024/10/30 · openalex updated_date 2026/07/28
In this paper, we investigate normal trees of directed graphs, which extend the fundamental concept of normal trees of undirected graphs. We prove that a directed graph D has a normal spanning tree if and only if the topological space |D| is metrizable, which generalises Diestel's result for undirected graphs. Furthermore, we show that the existence of normal arborescences implies the existence of normal trees in directed graphs, and that the converse is generally not true.