TY - JOUR

T1 - Blockers for Simple Hamiltonian Paths in Convex Geometric Graphs of Odd Order

AU - Keller, Chaya

AU - Perles, Micha A.

N1 - Publisher Copyright:
© 2019, Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2021/3/1

Y1 - 2021/3/1

N2 - Let G be a complete convex geometric graph, and let F be a family of subgraphs of G. A blocker for F is a set of edges, of smallest possible size, that has an edge in common with every element of 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) | = 2 m. 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) | = 2 m- 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.

AB - Let G be a complete convex geometric graph, and let F be a family of subgraphs of G. A blocker for F is a set of edges, of smallest possible size, that has an edge in common with every element of 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) | = 2 m. 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) | = 2 m- 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.

UR - http://www.scopus.com/inward/record.url?scp=85076117122&partnerID=8YFLogxK

U2 - 10.1007/s00454-019-00155-1

DO - 10.1007/s00454-019-00155-1

M3 - Article

AN - SCOPUS:85076117122

VL - 65

SP - 425

EP - 449

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

SN - 0179-5376

IS - 2

ER -