Blockers for noncrossing spanning trees in complete geometric graphs

Chaya Keller; Micha A. Perles; Eduardo Rivera-Campo; Virginia Urrutia-Galicia

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

Blockers for noncrossing spanning trees in complete geometric graphs

Chaya Keller
, Micha A. Perles
, Eduardo Rivera-Campo
, Virginia Urrutia-Galicia

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

5 Scopus citations

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.

Original language	English
Title of host publication	Thirty Essays on Geometric Graph Theory
Publisher	Springer New York
Pages	383-397
Number of pages	15
Volume	9781461401100
ISBN (Electronic)	9781461401100
ISBN (Print)	1461401097, 9781461401094
DOIs	https://doi.org/10.1007/978-1-4614-0110-0_20
State	Published - 1 Jul 2013
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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

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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.",

author = "Chaya Keller and Perles, \{Micha A.\} and Eduardo Rivera-Campo and Virginia Urrutia-Galicia",

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AU - Keller, Chaya

AU - Perles, Micha A.

AU - Rivera-Campo, Eduardo

AU - Urrutia-Galicia, Virginia

PY - 2013/7/1

Y1 - 2013/7/1

N2 - 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.

AB - 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.

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M3 - Chapter

AN - SCOPUS:84949176236

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BT - Thirty Essays on Geometric Graph Theory

PB - Springer New York

ER -

Blockers for noncrossing spanning trees in complete geometric graphs

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