4,570 research outputs found
A Coloring Algorithm for Disambiguating Graph and Map Drawings
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 algorithm computes a near optimal color assignment of a dual collision
graph, using a novel branch-and-bound procedure applied to a space
decomposition of the color gamut. We give examples demonstrating the
effectiveness of this approach in clarifying drawings of real world graphs and
maps
Products of Foldable Triangulations
Regular triangulations of products of lattice polytopes are constructed with
the additional property that the dual graphs of the triangulations are
bipartite. The (weighted) size difference of this bipartition is a lower bound
for the number of real roots of certain sparse polynomial systems by recent
results of Soprunova and Sottile [Adv. Math. 204(1):116-151, 2006]. Special
attention is paid to the cube case.Comment: new title; several paragraphs reformulated; 23 page
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