Covering by squares

Salinas, L.; Goles, E.

Abstract

In this paper we introduce the "do not touch" condition for squares in the discrete plane. We say that two squares "do not touch" if they do not share any vertex or any segment of an edge. Using this condition we define a covering of the discrete plane, the covering can be strong or weak, regular or non-regular. For simplicity, in this article, we will restrict our attention to regular coverings, i.e., only a size is allowed for the squares and all the squares have the same number of adjacent squares. We establish minimal conditions for the existence of a weak or strong regular covering of the discrete plane, and we give a bound for the number of adjacent squares with respect to the size of the squares in the regular covering. © 2007 Elsevier Ltd. All rights reserved.

Más información

Título según WOS: Covering by squares
Título según SCOPUS: Covering by squares
Título de la Revista: THEORETICAL COMPUTER SCIENCE
Volumen: 396
Número: 01-mar
Editorial: ELSEVIER SCIENCE BV
Fecha de publicación: 2008
Página de inicio: 10
Página final: 27
Idioma: English
URL: http://linkinghub.elsevier.com/retrieve/pii/S030439750700816X
DOI:

10.1016/j.tcs.2007.10.044

Notas: ISI, SCOPUS