Blockers for non-crossing spanning trees in complete geometric graphs
Chaya Keller, Micha A. Perles, Eduardo Rivera-Campo, Virginia, Urrutia-Galicia
TL;DR
This paper characterizes the minimal sets that block all simple spanning trees in complete geometric graphs, revealing how blocking SSTs of small diameter implies blocking all SSTs, especially in convex graphs.
Contribution
It provides a complete characterization of blockers for all simple spanning trees and establishes diameter-based conditions for blocking SSTs in geometric graphs.
Findings
Complete characterization of blockers for SSTs.
Blocking small-diameter SSTs implies blocking all SSTs.
Stronger results for convex geometric graphs.
Abstract
In this paper we present a complete characterization of the smallest sets that block all the simple spanning trees (SSTs) in a complete geometric graph. We also show that if a subgraph is a blocker for all SSTs of diameter at most 4, then it must block all simple spanning subgraphs, and in particular, all SSTs. For convex geometric graphs, we obtain an even stronger result: being a blocker for all SSTs of diameter at most 3 is already sufficient for blocking all simple spanning subgraphs.
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Taxonomy
TopicsAdvanced Graph Theory Research · Computational Geometry and Mesh Generation · Interconnection Networks and Systems