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Blockers for Simple Hamiltonian Paths in Convex Geometric Graphs of Odd Order

  • Chaya KellerEmail author
  • Micha A. Perles
Article
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Abstract

Let G be a complete convex geometric graph, and let \({\mathcal {F}}\) be a family of subgraphs of G. A blocker for \({\mathcal {F}}\) is a set of edges, of smallest possible size, that has an edge in common with every element of \({\mathcal {F}}\). In Keller and Perles (Discrete Comput Geom 60(1):1–8, 2018) we gave an explicit description of all blockers for the family of simple (i.e., non-crossing) Hamiltonian paths (SHPs) in G in the ‘even’ case \(|V(G)|=2m\). It turned out that all the blockers are simple caterpillar trees of a certain class. In this paper we give an explicit description of all blockers for the family of SHPs in the ‘odd’ case \(|V(G)|=2m-1\). In this case, the structure of the blockers is more complex, and in particular, they are not necessarily simple. Correspondingly, the proof is more complicated.

Notes

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Computer ScienceAriel UniversityArielIsrael
  2. 2.Einstein Institute of MathematicsHebrew UniversityJerusalemIsrael

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