It is shown that if a planar straight line graph (PSLG) with n vertices in general position in the plane can be augmented to a 3-edge-connected PSLG, then 2n−2 new edges are enough for the augmentation. This bound is tight: there are PSLGs with n ≥ 4 vertices such that any augmentation to a 3-edge-connected PSLG requires 2n− 2 new edges.

It is shown that every connected planar straight line graph with n ≥ 3 vertices has an embedding preserving augmentation to a 2-edge connected planar straight line graph with at most b(2n − 2)/3c new edges. It is also shown that every planar straight line tree with n ≥ 3 vertices has an embedding preserving augmentation to a 2-edge connected planar topological graph by adding at most bn/2c edge...

Familial prevalence of mitral valve prolapse in a Chinese population was determined in 22 propositi of whom 10 had straight back (group A), three had abnormally high metacarpal index (group B), and nine had neither (group C). Of 71 (32 male and 39 female subjects) first degree relatives screened, mitral valve prolapse was found in 19 (seven male and 12 female subjects) (26.8%). The familial pre...

background and aims: one of the main goals of standard orthodontic treatment is having the roots of teeth adjacent to extraction sites parallel to each other. the purpose of this study was to compare standard edgewise and preadjusted straight wire (mbt) methods in achieving this goal. materials and methods: for comparing root parallelism, 228 maxillary quadrants and 225 mandibular quadrants of ...

D eterrence is based on the notion that people consciously try to avoid pain and seek pleasure. It follows that by making a choice painful enough—such as the choice of crime—individuals will choose not to engage in the act. Across society as a whole, this perspective would predict that crime rates would be lowest in those places where offending evokes the most “pain” (or costs) and highest in t...

Straight skeleton (Angular Bisector Network, ABN) of a planar polygon, which can be grasped as a modi cation of a planar Voronoi diagram without parabolic arcs, has been successfully used by Oliva et al. [5] as a part of a system for three dimensional reconstruction of objects from a given set of 2D contours in parallel cross sections. The algorithm itself is used for the construction of interm...

A straight line triangle representation (SLTR) of a planar graph is a straight line drawing such that all the faces including the outer face have triangular shape. Such a drawing can be viewed as a tiling of a triangle using triangles with the input graph as skeletal structure. In this paper we present a characterization of graphs that have an SLTR. The charcterization is based on flat angle as...