On spanning tree packings of highly edge connected graphs
Florian Lehner
TL;DR
This paper refines a classical tree packing theorem for finite graphs and extends it to certain infinite graphs, providing new conditions for Hamiltonicity in line graphs of these graphs.
Contribution
It introduces a refined tree packing theorem applicable to infinite graphs and links it to Hamiltonicity conditions in line graphs.
Findings
Refined the Tutte/Nash-Williams tree packing theorem for finite graphs.
Extended the theorem to end faithful spanning tree packings in infinite graphs.
Established a sufficient Hamiltonicity condition for line graphs of these infinite graphs.
Abstract
We prove a refinement of the tree packing theorem by Tutte/Nash-Williams for finite graphs. This result is used to obtain a similar result for end faithful spanning tree packings in certain infinite graphs and consequently to establish a sufficient Hamiltonicity condition for the line graphs of such graphs.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph theory and applications · Limits and Structures in Graph Theory