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On the Intersection Number of Matchings and Minimum Weight Perfect Matchings of Multicolored Point Sets

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Abstract

Let P and Q be disjoint point sets with 2r and 2s elements respectively, and M1 and M2 be their minimum weight perfect matchings (with respect to edge lengths). We prove that the edges of M1 and M2 intersect at most |M1|+|M2|−1 times. This bound is tight. We also prove that P and Q have perfect matchings (not necessarily of minimum weight) such that their edges intersect at most min{r,s} times. This bound is also sharp.

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Authors and Affiliations

  1. Instituto de Matemáticas, Universidad Nacional Autónoma de México, México, D.F., México

    Criel Merino & Jorge Urrutia

  2. Instituto de Investigación en Comunicación Óptica, Universidad Autónoma de San Luis Potosí, San Luis Potosí, México

    Gelasio Salazar

Authors
  1. Criel Merino
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  2. Gelasio Salazar
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  3. Jorge Urrutia
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Corresponding authors

Correspondence to Criel Merino, Gelasio Salazar or Jorge Urrutia.

Additional information

Supported by PAPIIT(UNAM) of México, Proyecto IN110802

Supported by FAI-UASLP and by CONACYT of México, Proyecto 32168-E

Supported by CONACYT of México, Proyecto 37540-A

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Merino, C., Salazar, G. & Urrutia, J. On the Intersection Number of Matchings and Minimum Weight Perfect Matchings of Multicolored Point Sets. Graphs and Combinatorics 21, 333–341 (2005). https://doi.org/10.1007/s00373-004-0606-8

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  • DOI: https://doi.org/10.1007/s00373-004-0606-8

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