The set of all orientations of a planar graph with prescribed outdegrees carries the structure of a distributive lattice. This general theorem is proven in the first part of the p...
We introduce a new measure for planar point sets S that captures a combinatorial distance that S is from being a convex set: The reflexivity (S) of S is given by the smallest numb...
Let G be an embedded planar graph whose edges may be curves. For two arbitrary points of G, we can compare the length of the shortest path in G connecting them against their Euclid...