Blockers for Noncrossing Spanning Trees in Complete Geometric Graphs

Chaya Keller (), Micha A. Perles (), Eduardo Rivera-Campo () and Virginia Urrutia-Galicia ()
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Chaya Keller: Hebrew University, Einstein Institute of Mathematics
Micha A. Perles: Hebrew University, Einstein Institute of Mathematics
Eduardo Rivera-Campo: Universidad Autónoma Metropolitana-Iztapalapa, Departamento de Matemáticas
Virginia Urrutia-Galicia: Universidad Autónoma Metropolitana-Iztapalapa, Departamento de Matemáticas

A chapter in Thirty Essays on Geometric Graph Theory, 2013, pp 383-397 from Springer

Abstract: Abstract In this chapter, 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.

Keywords: Span Tree; General Position; Boundary Edge; Relative Interior; Boundary Vertex (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-0110-0_20

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DOI: 10.1007/978-1-4614-0110-0_20

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