We show that the hit-and-run random walk mixes rapidly starting from any interior point of a convex body. This is the first random walk known to have this property. In contrast, t...
We analyze a randomized version of the Brelaz heuristic on sparse random graphs. We prove that almost all graphs with average degree dp4:03; i.e., G?n; p ? d=n?; are 3-colorable a...
d abstract) Thomas Feierl⋆ Fakult¨at f¨ur Mathematik Universit¨at Wien Nordbergstr. 15 1090 Wien, Austria Abstract. We determine the weak limit of the distribution of the rand...
We study line systems in metric spaces induced by graphs. A line is a subset of vertices defined by a relation of betweeness. We show that the class of all graphs having exactly k ...
We show that a random walk on a tournament on n vertices finds either a sink or a 3-cycle in expected time O √ n · log n · log∗ n , that is, sublinear both in the size of th...