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

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Abstract

Let G be a complete convex geometric graph on 2m vertices, 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 meets every element of \(\mathcal {F}\). 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).

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References

  1. Brass, P., Károlyi, G., Valtr, P.: A Turán-type extremal theory of convex geometric graphs. In: Aronov, B., et al. (eds.) Discrete and Computational Geometry. Algorithms and Combinatorics, vol. 25, pp. 275–300. Springer, Berlin (2003)

    Chapter  Google Scholar 

  2. Capoyleas, V., Pach, J.: A Turán-type theorem on chords of convex polygons. J. Comb. Theory Ser. B 56(1), 9–15 (1992)

    Article  MATH  Google Scholar 

  3. Harary, F., Schwenk, A.J.: The number of caterpillars. Discrete Math. 6, 359–365 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  4. Keller, C., Perles, M.A.: On the smallest sets blocking simple perfect matchings in a convex geometric graph. Isr. J. Math. 187, 465–484 (2012)

  5. Kupitz, Y.S.: Extremal Problems in Combinatorial Geometry. Lecture Notes Series, vol. 53. Aarhus University, Aarhus (1979)

    MATH  Google Scholar 

  6. Kupitz, Y.S., Perles, M.A.: Extremal theory for convex matchings in convex geometric graphs. Discrete Comput. Geom. 15(2), 195–220 (1996)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The research of C. Keller was partially supported by Grant 635/16 from the Israel Science Foundation, by the Shulamit Aloni Post-Doctoral Fellowship of the Israeli Ministry of Science and Technology, by the Kreitman Foundation Post-Doctoral Fellowship, and by the Hoffman Leadership and Responsibility Program at the Hebrew University.

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Authors and Affiliations

  1. Department of Mathematics, Ben-Gurion University of the NEGEV, Beersheba, Israel

    Chaya Keller

  2. Einstein Institute of Mathematics, Hebrew University, 9190401, Jerusalem, Israel

    Micha A. Perles

Authors
  1. Chaya Keller
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  2. Micha A. Perles
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Correspondence to Chaya Keller.

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Editor in Charge: János Pach

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Keller, C., Perles, M.A. Blockers for Simple Hamiltonian Paths in Convex Geometric Graphs of Even Order. Discrete Comput Geom 60, 1–8 (2018). https://doi.org/10.1007/s00454-017-9921-8

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  • DOI: https://doi.org/10.1007/s00454-017-9921-8

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