Listing spanning trees of outerplanar graphs by pivot-exchanges
Nastaran Behrooznia, Torsten M\"utze

TL;DR
This paper presents an efficient method to list all spanning trees of outerplanar graphs with minimal edge exchanges, forming Hamilton paths on the associated 0/1-polytope, and introduces a greedy algorithm for this purpose.
Contribution
It introduces a simple greedy algorithm to list spanning trees of outerplanar graphs with minimal edge exchanges, efficiently generating Hamilton paths on the spanning tree polytope.
Findings
Listings can be generated in O(n log n) time per tree.
Consecutive spanning trees differ by an exchange of two edges sharing an endpoint.
The listings form Hamilton paths on the spanning tree polytope.
Abstract
We prove that the spanning trees of any outerplanar triangulation can be listed so that any two consecutive spanning trees differ in an exchange of two edges that share an end vertex. For outerplanar graphs with faces of arbitrary lengths (not necessarily 3) we establish a similar result, with the condition that the two exchanged edges share an end vertex or lie on a common face. These listings of spanning trees are obtained from a simple greedy algorithm that can be implemented efficiently, i.e., in time per generated spanning tree, where is the number of vertices of . Furthermore, the listings correspond to Hamilton paths on the 0/1-polytope that is obtained as the convex hull of the characteristic vectors of all spanning trees of .
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Taxonomy
TopicsAdvanced Graph Theory Research · Stochastic processes and statistical mechanics · Graph theory and applications
