Recently, Aichholzer, García, Orden, and Ramos derived a remarkably improved lower bound for the number of (⩽k)-edges in an n-point set, and as an immediate corollary, an improved lower bound on the rectilinear crossing number of Kn. We use simple all . . .

Let G(v,δ) be the set of all δ-regular graphs on v vertices. Certain graphs from among those in G(v,δ) with maximum girth have a special property called trace-minimality. In particular, all strongly regular graphs with no triangles and some cages are . . .

Devadoss asked: (1) can every polygon be convexified so that no internal visibility (between vertices) is lost in the process? Moreover, (2) does such a convexification exist, in which exactly one vertex is moved at a time (that is, using single-verte . . .

"Consider a k-element subset P of the plane. It is known that the maximum number of sets similar to P that can be found among n points in the plane is Θ(n2) if and only if the cross ratio of any quadruplet of points in P is algebraic [3], [9]. In this . . .

Let f(n) be the maximum number of unit distances determined by the vertices of a convex n -gon. Erdos and Moser conjectured that this function is linear. Supporting this conjecture we prove that f sym (n) ∼∼ 2n where f sym (n) is the restriction of f( . . .

Let P be a set of points in general position in the plane. Join all pairs of points in P with straight line segments. The number of segment-crossings in such a drawing, denoted by cr(P) , is the rectilinear crossing number of P. A halving line of P is . . .

Let P be a set of n points in the plane. A geometric proximity graph on P is a graph where two points are connected by a straight-line segment if they satisfy some prescribed proximity rule. We consider four classes of higher order proximity graphs, n . . .

We give a new lower bound for the rectilinear crossing number of the complete geometric graph K n . We prove that and we extend the proof of the result to pseudolinear drawings of K n .

Physical understanding of total and spectral solar irradiance variation depends upon establishing a connection between the temporal variability of spatially resolved solar structures and spacecraft observations of irradiance. One difficulty in compari . . .

Resistance to heavy metals is important for the survival of bacteria in contaminated environments. In this study, we show that the unicellular cyanobacterial species Synechococcus sp. IU 625 adapts to growth in the presence of mercuric chloride, recov . . .