# Blockers for Simple Hamiltonian Paths in Convex Geometric Graphs of Even Order

Blockers for Simple Hamiltonian Paths in Convex Geometric Graphs of Even Order Let G be a complete convex geometric graph on 2m vertices, and let $$\mathcal {F}$$ F be a family of subgraphs of G. A blocker for $$\mathcal {F}$$ F is a set of edges, of smallest possible size, that meets every element of $$\mathcal {F}$$ F . In Keller and Perles (Israel J Math 187:465–484, 2012) we gave an explicit description of all blockers for the family of simple perfect matchings (SPMs) of G. In this paper we show that the family of simple Hamiltonian paths in G has exactly the same blockers as the family of SPMs. Our argument is rather short, and provides a much simpler proof of the result of Keller and Perles (2012). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Discrete & Computational Geometry Springer Journals

# Blockers for Simple Hamiltonian Paths in Convex Geometric Graphs of Even Order

, Volume 60 (1) – Aug 9, 2017
8 pages
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Publisher
Springer US
Copyright
Copyright © 2017 by Springer Science+Business Media, LLC
Subject
Mathematics; Combinatorics; Computational Mathematics and Numerical Analysis
ISSN
0179-5376
eISSN
1432-0444
D.O.I.
10.1007/s00454-017-9921-8
Publisher site
See Article on Publisher Site

### Abstract

Let G be a complete convex geometric graph on 2m vertices, and let $$\mathcal {F}$$ F be a family of subgraphs of G. A blocker for $$\mathcal {F}$$ F is a set of edges, of smallest possible size, that meets every element of $$\mathcal {F}$$ F . In Keller and Perles (Israel J Math 187:465–484, 2012) we gave an explicit description of all blockers for the family of simple perfect matchings (SPMs) of G. In this paper we show that the family of simple Hamiltonian paths in G has exactly the same blockers as the family of SPMs. Our argument is rather short, and provides a much simpler proof of the result of Keller and Perles (2012).

### Journal

Discrete & Computational GeometrySpringer Journals

Published: Aug 9, 2017

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