 
Summary: Matching points with squares
Bernardo M. ´Abrego1
Esther M. Arkin2
Silvia Fern´andezMerchant1
Ferran Hurtado3
Mikio Kano4
Joseph S. B. Mitchell2
Jorge Urrutia5
May 30, 2008
Abstract
Given a class C of geometric objects and a point set P, a Cmatching of P is a set M =
{C1, . . . , Ck} C of elements of C such that each Ci contains exactly two elements of P and
each element of P lies in at most one Ci. If all of the elements of P belong to some Ci, M
is called a perfect matching. If, in addition, all of the elements of M are pairwise disjoint, we
say that this matching M is strong. In this paper we study the existence and characteristics of
Cmatchings for point sets in the plane when C is the set of isothetic squares in the plane. A
consequence of our results is a proof that the Delaunay triangulations for the L metric and
the L1 metric always admit a Hamiltonian path.
1 Introduction
Let C be a class of geometric objects and let P be a point set with an even number, n, of elements
