Happy endings for flip graphs

We show that the triangulations of a finite point set form a flip graph that can be embedded isometrically into a hypercube, if and only if the point set has no empty convex pentagon. Point sets of this type include convex subsets of lattices, points on two lines, and several other infinite families. As a consequence, flip distance in such point sets can be computed efficiently.Comment: 26 pages, 15 figures. Revised and expanded for journal publicatio

Subquadratic nonobtuse triangulation of convex polygons

A convex polygon with n sides can be triangulated by O(n^1.85) triangles, without any obtuse angles. The construction uses a novel form of geometric divide and conquer

Densities of Minor-Closed Graph Families

We define the limiting density of a minor-closed family of simple graphs F to be the smallest number k such that every n-vertex graph in F has at most kn(1+o(1)) edges, and we investigate the set of numbers that can be limiting densities. This set of numbers is countable, well-ordered, and closed; its order type is at least {\omega}^{\omega}. It is the closure of the set of densities of density-minimal graphs, graphs for which no minor has a greater ratio of edges to vertices. By analyzing density-minimal graphs of low densities, we find all limiting densities up to the first two cluster points of the set of limiting densities, 1 and 3/2. For multigraphs, the only possible limiting densities are the integers and the superparticular ratios i/(i+1).Comment: 19 pages, 4 figure

[Rezension zu:] Mark Kopytman - Voices of Memories: Essays and Dialogues, ed. Yulia Kreinin, Israel Music Institute, Tel Aviv, 2004, 288 p.

Mark Kopytman - Voices of Memories: Essays and Dialogues, ed. Yulia Kreinin, Israel Music Institute, Tel Aviv, 2004, 288 p. A Doctor of Medicine who is also a composer is a rarity. A composer who is also a Doctor of Medicine is even rarer. Dr. Med. Mark Kopytman, however, is above all a composer, and one of Israel´s foremost contemporary composers at that. "Mark Kopytman - Voices of Memories" is a Festschrift - a volume of collected essays edited by Yulia Kreinin, to celebrate his 70th birthday. It is a formidable literary monument to honour this outstanding personality

Cubic Partial Cubes from Simplicial Arrangements

We show how to construct a cubic partial cube from any simplicial arrangement of lines or pseudolines in the projective plane. As a consequence, we find nine new infinite families of cubic partial cubes as well as many sporadic examples.Comment: 11 pages, 10 figure