
TL;DR
This paper explores the concept of normal trees in directed graphs, establishing conditions for their existence and generalizing known results from undirected graphs to directed ones.
Contribution
It introduces the notion of normal trees for directed graphs, proves their existence under certain topological conditions, and compares them with normal arborescences.
Findings
Directed graphs have normal spanning trees iff their topological space is metrizable.
Existence of normal arborescences implies normal trees, but not vice versa.
Generalizes Diestel's result from undirected to directed graphs.
Abstract
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 has a normal spanning tree if and only if the topological space 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.
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Taxonomy
TopicsGraph Labeling and Dimension Problems · Advanced Graph Theory Research
