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Mathematics > Combinatorics

arXiv:1805.02933 (math)
[Submitted on 8 May 2018 (v1), last revised 3 Apr 2020 (this version, v3)]

Title:An analogue of Edmonds' Branching Theorem for infinite digraphs

Authors:J. Pascal Gollin, Karl Heuer
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Abstract:We extend Edmonds' Branching Theorem to locally finite infinite digraphs. As examples of Oxley or Aharoni and Thomassen show, this cannot be done using ordinary arborescences, whose underlying graphs are trees. Instead we introduce the notion of pseudo-arborescences and prove a corresponding packing result. Finally, we verify some tree-like properties for these objects, but give also an example that their underlying graphs do in general not correspond to topological trees in the Freudenthal compactification of the underlying multigraph of the digraph.
Comments: 15 pages, 1 figure; only minor changes to metadata
Subjects: Combinatorics (math.CO)
MSC classes: 05C63, 05C20 (Primary), 05C70 (Secondary)
Cite as: arXiv:1805.02933 [math.CO]
  (or arXiv:1805.02933v3 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.1805.02933

Submission history

From: Karl Heuer [view email]
[v1] Tue, 8 May 2018 10:30:21 UTC (29 KB)
[v2] Tue, 10 Sep 2019 16:27:04 UTC (25 KB)
[v3] Fri, 3 Apr 2020 11:34:18 UTC (25 KB)
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