Abstract
In this paper we present a complete characterization of the smallest sets which block all the simple perfect matchings in a complete convex geometric graph on 2m vertices. In particular, we show that all these sets are caterpillar graphs with a special structure, and that their total number is m·2m−1.
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References
F. Harary and A. J. Schwenk, The number of caterpillars, Discrete Mathematics 6 (1973), 359–365.
Y. S. Kupitz, Extremal Problems of Combinatorial Geometry, Aarhus University Lecture Notes Series 53 (1979).
M. A. Perles, unpublished.
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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). https://doi.org/10.1007/s11856-011-0090-9
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DOI: https://doi.org/10.1007/s11856-011-0090-9