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Author Salinas, L.; Goles, E.
Title Covering by squares Type
Year 2008 Publication Theoretical Computer Science Abbreviated Journal Theor. Comput. Sci.
Volume 396 Issue 1-3 Pages 10-27
Keywords discrete geometry; covering; tiling
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. (C) 2007 Elsevier B.V. All rights reserved.
Address [Salinas, L.] Univ Chile, Dept Engn Math, Santiago, Chile, Email: lsalinas@dim.uchile.cl
Corporate Author Thesis
Publisher Elsevier Science Bv Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0304-3975 ISBN Medium
Area Expedition Conference
Notes WOS:000256199100002 Approved
Call Number UAI @ eduardo.moreno @ Serial 31
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