Displaying similar documents to “Packing unit squares in squares: A survey and new results.”

Translative packing of a square with sequences of squares

Janusz Januszewski (2010)

Colloquium Mathematicae

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Let S be a square and let S' be a square of unit area with a diagonal parallel to a side of S. Any (finite or infinite) sequence of homothetic copies of S whose total area does not exceed 4/9 can be packed translatively into S'.

On-line Packing Squares into n Unit Squares

Janusz Januszewski (2010)

Bulletin of the Polish Academy of Sciences. Mathematics

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If n ≥ 3, then any sequence of squares of side lengths not greater than 1 whose total area does not exceed ¼(n+1) can be on-line packed into n unit squares.

Universal container for packing rectangles

Janusz Januszewski (2002)

Colloquium Mathematicae

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The aim of the paper is to find a rectangle with the least area into which each sequence of rectangles of sides not greater than 1 with total area 1 can be packed.

Packing Parameters in Graphs

I. Sahul Hamid, S. Saravanakumar (2015)

Discussiones Mathematicae Graph Theory

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In a graph G = (V,E), a non-empty set S ⊆ V is said to be an open packing set if no two vertices of S have a common neighbour in G. An open packing set which is not a proper subset of any open packing set is called a maximal open packing set. The minimum and maximum cardinalities of a maximal open packing set are respectively called the lower open packing number and the open packing number and are denoted by ρoL and ρo. In this paper, we present some bounds on these parameters. ...