We introduce a new notion for geometric families called self-coverability and show that homothets of convex polygons are self-coverable. As a corollary, we obtain several results about coloring point sets such that any member of the family with many points contains all colors. This is dual (and in some cases equivalent) to the much investigated cover-decomposability problem
We consider the problem of 2-coloring geometric hypergraphs. Specifically, we show that there is a c...
AbstractIn this paper, we address the problem of covering points with orthogonally convex polygons. ...
A set ${ cal P} = P sb1,P sb2, ...,P sb{k}$ of polygons is called a k-cover of a simple polygon P if...
A planar set P is said to be cover-decomposable if there is a constant k = k(P) such that every k-fo...
The goal of this paper is to give a new, abstract approach to cover-decomposition and polychromatic ...
The goal of this paper is to give a new, abstract approach to cover-decomposition and polychromatic ...
We show that for any concave polygon that has no parallel sides and for any k, there is a k-fold cov...
We consider the problem of 2-coloring geometric hypergraphs. Specifically, we show that there is a c...
We study whether for a given planar family F there is an m such that any finite set of points can be...
We study two decomposition problems in combinatorial geometry. The rst part of the thesis deals with...
Abstract. We give new positive results on the long-standing open problem of geometric covering decom...
We prove that octants are cover-decomposable into multiple coverings, i.e., for any k there is an ...
We study whether for a given planar family F there is an m such that any finite set of points can be...
A system of sets forms an m-fold covering of a set X if every point of X belongs to at least m of it...
A system of sets forms an m-fold covering of a set X if every point of X belongs to at least m of it...
We consider the problem of 2-coloring geometric hypergraphs. Specifically, we show that there is a c...
AbstractIn this paper, we address the problem of covering points with orthogonally convex polygons. ...
A set ${ cal P} = P sb1,P sb2, ...,P sb{k}$ of polygons is called a k-cover of a simple polygon P if...
A planar set P is said to be cover-decomposable if there is a constant k = k(P) such that every k-fo...
The goal of this paper is to give a new, abstract approach to cover-decomposition and polychromatic ...
The goal of this paper is to give a new, abstract approach to cover-decomposition and polychromatic ...
We show that for any concave polygon that has no parallel sides and for any k, there is a k-fold cov...
We consider the problem of 2-coloring geometric hypergraphs. Specifically, we show that there is a c...
We study whether for a given planar family F there is an m such that any finite set of points can be...
We study two decomposition problems in combinatorial geometry. The rst part of the thesis deals with...
Abstract. We give new positive results on the long-standing open problem of geometric covering decom...
We prove that octants are cover-decomposable into multiple coverings, i.e., for any k there is an ...
We study whether for a given planar family F there is an m such that any finite set of points can be...
A system of sets forms an m-fold covering of a set X if every point of X belongs to at least m of it...
A system of sets forms an m-fold covering of a set X if every point of X belongs to at least m of it...
We consider the problem of 2-coloring geometric hypergraphs. Specifically, we show that there is a c...
AbstractIn this paper, we address the problem of covering points with orthogonally convex polygons. ...
A set ${ cal P} = P sb1,P sb2, ...,P sb{k}$ of polygons is called a k-cover of a simple polygon P if...
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