Orientations of infinite graphs
Marcel Koloschin, Max Pitz
TL;DR
This paper extends Nash-Williams' orientation theorem from finite to infinite multigraphs, demonstrating that highly edge-connected infinite graphs can also be oriented to preserve connectivity.
Contribution
It proves that Nash-Williams' orientation theorem applies to all infinite multigraphs, broadening the scope of the original finite graph result.
Findings
The theorem holds for all infinite multigraphs.
Infinite graphs with high edge connectivity can be oriented to maintain connectivity.
Extends finite graph orientation results to infinite cases.
Abstract
Building on recent work by Thomassen, we show that Nash-Williams' orientation theorem, that every finite -edge-connected multigraph has a -arc-connected orientation, also holds for all infinite multigraphs.
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Taxonomy
TopicsAdvanced Graph Theory Research · Limits and Structures in Graph Theory · Advanced Topology and Set Theory