منابع مشابه
Stationary map coloring
We consider a planar Poisson process and its associated Voronoi map. We show that there is a proper coloring with 6 colors of the map which is a deterministic isometry-equivariant function of the Poisson process. As part of the proof we show that the 6-core of the corresponding Delaunay triangulation is empty. Generalizations, extensions and some open questions are discussed.
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1. INTRODUCTION. Suppose that Alice wants to color a planar map using four colors in a proper way, that is, so that any two adjacent regions get different colors. Despite the fact that she knows for certain that it is eventually possible, she may fail in her first attempts. Indeed, there are usually many proper partial colorings not extend-able to proper colorings of the whole map. Thus, if she...
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We obtain strong coloring theorems at successors of singular cardinals from failures of certain instances of simultaneous reflection of stationary sets. Along the way, we establish new results in club-guessing and in the general theory of ideals.
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After a brief discussion of the history of the problem, we propose a generalization of the map colouring problem to higher dimensions. The map colouring problem was originally posed by Francis Guthrie in 1852. It asks for the minimum number of colours required to colour all possible maps (real or imagined) if one wishes to ensure that neighbouring countries receive different colours. Clearly on...
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Abstract. Drawings of non-planar graphs always result in edge crossings. When there are many edges crossing at small angles, it is often difficult to follow these edges, because of the multiple visual paths resulted from the crossings that slow down eye movements. In this paper we propose an algorithm that disambiguates the edges with automatic selection of distinctive colors. Our proposed algo...
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ژورنال
عنوان ژورنال: Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
سال: 2012
ISSN: 0246-0203
DOI: 10.1214/10-aihp399