(1) Division de Ciencas Basicas e Ingeniera [Azcapotzalco]
(2) Instituto de Matematicas [México]
(3) Instituto de Matemáticas [México]
(4) Centro de Investigacion y de Estudios Avanzados del Instituto Politécnico Nacional
(5) Departamento de Matematicas [Mexico]
(6) Facultad de Ciencas [Mexico]
(7) Departament de Matemàtica Aplicada II
(8) Escuela Superior de Fisica y Matematicas [Mexico]
Abstract
Let P be a set of n points in general position in the plane. A subset I of P is called an island if there exists a convex set C such that I = P \C. In this paper we define the generalized island Johnson graph of P as the graph whose vertex consists of all islands of P of cardinality k, two of which are adjacent if their intersection consists of exactly l elements. We show that for large enough values of n, this graph is connected, and give upper and lower bounds on its diameter.
