The physics of custody

  • Andrés Gomberoff
  • Víctor Muñoz
  • Pierre Paul Romagnoli
Regular Article


Divorced individuals face complex situations when they have children with different ex-partners, or even more, when their new partners have children of their own. In such cases, and when kids spend every other weekend with each parent, a practical problem emerges: is it possible to have such a custody arrangement that every couple has either all of the kids together or no kids at all? We show that in general, it is not possible, but that the number of couples that do can be maximized. The problem turns out to be equivalent to finding the ground state of a spin glass system, which is known to be equivalent to what is called a weighted max-cut problem in graph theory, and hence it is NP-complete.


Statistical and Nonlinear Physics 

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Andrés Gomberoff
    • 1
  • Víctor Muñoz
    • 2
  • Pierre Paul Romagnoli
    • 3
  1. 1.Departamento de Ciencias FísicasUniversidad Andres BelloSantiagoChile
  2. 2.Departamento de Física, Facultad de CienciasUniversidad de ChileSantiagoChile
  3. 3.Departamento de MatemáticasUniversidad Andres BelloSantiagoChile

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