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  • Work
    Article
    Keszegh, Balazs
    Given n points in the plane, a covering path is a polygonal path that visits all the points. If no three points are collinear, every covering path requires at least n/2 segments, and n−1 straight line segments obviously suffice even if the covering pa . . .
  • Work
    Article
    Ruiz-Vargas, Andres J.
    It is shown that for a constant t∈N, every simple topological graph on n vertices has O(n)edges if the graph has no two sets of t edges such that every edge in one set is disjoint from all edges of the other set (i.e., the complement of the intersecti . . .
  • Work
    Article
    Korman, Matias
    We study biplane graphs drawn on a finite planar point set \(S\) in general position. This is the family of geometric graphs whose vertex set is \(S\) and can be decomposed into two plane graphs. We show that two maximal biplane graphs—in the sense th . . .
  • Work
    Article
    Toth, Csaba D.
    BACKGROUND: As injury rates rise in the later stages of sporting activities, a better understanding of lower extremity biomechanics in the later phases of gamelike situations may improve training and injury prevention programs. HYPOTHESIS: Lower extre . . .
  • Work
    Article
    Dumitrescu, Adrian
    Let S be a set of n points in the unit square [,1]2, one of which is the origin. We construct n pairwise interior-disjoint axis-aligned empty rectangles such that the lower left corner of each rectangle is a point in S, and the rectangles jointly cove . . .
  • Work
    Article
    Fox-Epstein, Eli
    It is shown that every simple polygon in general position with n walls can be illuminated from a single point light source s after at most \(\lfloor (n-2)/4\rfloor \)diffuse reflections, and this bound is the best possible. A point s with this propert . . .
  • Work
    Article
    Szekely, Laszlo A.
    he crossing number cr(G) of a graph G = (V , E) is the smallest number of edge crossings over all drawings of G in the plane. For any k ≥ 1, the k-planar crossing number of G, crk(G), is defined as the minimum of cr(G0) + cr(G1) + ... + cr(Gk−1) over a . . .
  • Work
    Article
    Wood, David
    A mixed plane graph is a plane graph whose edge set is partitioned into a set of directed edges and a set of undirected edges. An orientation of a mixed plane graph G is an assignment of directions to the undirected edges of G resulting in a directed . . .
  • Work
    Article
    Dumitrescu, Adrian
    For points in the unit square , an anchored rectangle packing consists of interior-disjoint axis-aligned empty rectangles such that point is a corner of the rectangle (that is, is anchored at ) for . We show that for every set of points in , there is . . .
  • Work
    Article
    Toth, Csaba D.
    For two planar convex bodies, C and D , consider a packing S of n positive homothets of C contained in D . We estimate the total perimeter of the bodies in S , denoted per(S) , in terms of per(D) and n . When all homothets of C touch the boundary of t . . .