منابع مشابه
Coloring Complexes and Arrangements
Steingrimsson’s coloring complex and Jonsson’s unipolar complex are interpreted in terms of hyperplane arrangements. This viewpoint leads to short proofs that all coloring complexes and a large class of unipolar complexes have convex ear decompositions. These convex ear decompositions impose strong new restrictions on the chromatic polynomials of all finite graphs.
متن کاملColoring and Guarding Arrangements
Given an arrangement of lines in the plane, what is the minimum number c of colors required to color the lines so that no cell of the arrangement is monochromatic? In this paper we give bounds on the number c, as well as some of its variations. We cast these problems as characterizing the chromatic and the independence numbers of a new family of geometric hypergraphs.
متن کاملA Note on Coloring Line Arrangements
We show that the lines of every arrangement of n lines in the plane can be colored with O( √ n/ log n) colors such that no face of the arrangement is monochromatic. This improves a bound of Bose et al. by a Θ( √ log n) factor. Any further improvement on this bound would also improve the best known lower bound on the following problem of Erdős: estimate the maximum number of points in general po...
متن کاملHypergraph coloring complexes
The aim of this paper is to generalize the notion of the coloring complex of a graph to hypergraphs. We present three different interpretations of those complexes-a purely combinatorial one and two geometric ones. It is shown, that most of the properties, which are known to be true for coloring complexes of graphs, break down in this more general setting, e.g., Cohen-Macaulayness and partitiona...
متن کاملRegularized arrangements of cellular complexes
In this paper we propose a novel algorithm to combine two or more cellular complexes, providing a minimal fragmentation of the cells of the resulting complex. We introduce here the idea of arrangement generated by a collection of cellular complexes, producing a cellular decomposition of the embedding space. e algorithm that executes this computation is called Merge of complexes. e arrangement...
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2007
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-007-0086-z