This paper is part of an ongoing endeavor to bring the theory of fair division closer to
practice by handling requirements from real-life applications. We focus on two requirements …

In this survey the following types of colorings of plane graphs are discussed, both in their
vertex and edge versions: facially proper coloring, rainbow coloring, antirainbow coloring …

Polychromatic 4-coloring of cubic bipartite plane graphs - ScienceDirect Skip to main
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A rectangular partition is a partition of a plane rectangle into an arbitrary number of non-
overlapping rectangles such that no four rectangles share a corner. In this note, it is proven …

A strong hyperbox-respecting coloring of an n-dimensional hyperbox partition is a coloring
of the corners of its hyperboxes with 2 n colors such that any hyperbox has all the colors …

We study three problems in combinatorial geometry. The problems investigated are conflict-
free colorings of point sets in the plane with few colors, polychromatic colorings of the …

It is well-known that every triangulation on a closed surface F^ 2 F 2 has a spanning
quadrangulation Q, and in particular, Q is bipartite if F^ 2 F 2 is the sphere. In other words …

A general (rectangular) partition is a partition of a rectangle into an arbitrary number of non-
overlapping subrectangles. This paper examines vertex 4-colorings of general partitions …

A (not necessarily proper) k-coloring c: V (G)→{1, 2,… k} of a graph G on a surface is a facial
t-complete k-coloring if every t-tuple of colors appears on the boundary of some face of G …

A non-degenerate rectangular subdivision is a subdivision of a rectangle into a set of non-
overlapping rectangles S, such that no four rectangles meet in a point. We consider a …