An equitable coloring of a graph is a proper vertex coloring such that the sizes of any two color classes differ by at most one. The least positive integer k for which there exis...
We study a switch Markov chain on regular graphs, where switches are allowed only between links that are at distance 3; we call this the Flip. The motivation for studying the Flip...
We study a random graph Gn that combines certain aspects of geometric random graphs and preferential attachment graphs. The vertices of Gn are n sequentially generated points x1, ...
We consider a consensus algorithm in which every node in a time-varying undirected connected graph assigns equal weight to each of its neighbors. Under the assumption that the deg...
We give a polynomial-time algorithm for the following problem: Given a degree sequence in which each degree is bounded from above by a constant, select, uniformly at random, an un...