Eur. Phys. J. B (2014) 87: 37
https://doi.org/10.1140/epjb/e2014-40666-7

Regular Article

The physics of custody

¹ Universidad Andres Bello, Departamento de Ciencias Físicas, Av. República 252, 8370251 Santiago, Chile
² Departamento de Física, Facultad de Ciencias, Universidad de Chile, Santiago, Chile
³ Universidad Andres Bello, Departamento de Matemáticas, Av. República 252, 8370251 Santiago, Chile

^a e-mail: agomberoff@unab.cl

Received: 11 July 2013
Received in final form: 16 December 2013
Published online: 10 February 2014

Abstract

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.