We consider the problem of finding a sparse set of edges containing the minimum spanning tree (MST) of a random subgraph of G with high probability. The two random models that we ...
Abstract. We present an expected polynomial time algorithm to generate a labeled planar graph uniformly at random. To generate the planar graphs, we derive recurrence formulas that...
We introduce the notion of Lombardi graph drawings, named after the abstract artist Mark Lombardi. In these drawings, edges are represented as circular arcs rather than as line seg...
Christian A. Duncan, David Eppstein, Michael T. Go...
We consider the problem of learning a general graph using edge-detecting queries. In this model, the learner may query whether a set of vertices induces an edge of the hidden grap...
We find the asymptotic number of connected graphs with k vertices and k - 1 + l edges when k, l approach infinity, reproving a result of Bender, Canfield and McKay. We use the pro...