Edge degeneracy: Algorithmic and structural results

Rank-width: Algorithmic and structural results

Rank-width is a width parameter of graphs describing whether it is possible to decompose a graph into a tree-like structure by ‘simple’ cuts. This survey aims to summarize known algorithmic and structural results on rank-width of graphs.

Steepest Edge , Degeneracy and Conditioning in LPbyR

Steepest edge criteria have often been shown to work well in Simplex or Active Set methods for Linear Programming (LP). It is therefore important that any technique for resolving degeneracy in LP should conveniently be able to use steepest edge criteria in the selection of the search direction. A recursive technique for resolving degeneracy 5] is of some interest in that it provides a guarantee...

Folding a Triangulated Simple Polygon: Structural and Algorithmic Results

We describe a linear-time algorithm that folds a triangulated simple polygon into a single triangle. Using this technique, we derive a particularly simple proof of Chvv atal's art gallery theorem and improve or simplify a number of algorithms that deal with triangulated simple polygons. We describe two improved algorithms, both based on the degree sequence of the boundary vertices of the given ...

Structural Basis of Specificity and Degeneracy

Triangle-Free Penny Graphs: Degeneracy, Choosability, and Edge Count

We show that triangle-free penny graphs have degeneracy at most two, list coloring number (choosability) at most three, diameter D = Ω( √ n), and at most min ( 2n−Ω( √ n), 2n−D − 2 ) edges.