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...
An old problem of Erd˝os, Fajtlowicz and Staton asks for the order of a largest induced regular subgraph that can be found in every graph on n vertices. Motivated by this problem...
Michael Krivelevich, Benny Sudakov, Nicholas C. Wo...
: We study a model of random uniform hypergraphs, where a random instance is obtained by adding random edges to a large hypergraph of a given density. The research on this model fo...
In this paper, we prove that there exists a function k = (4 + o(1))k such that G(n, /n) contains a k-regular graph with high probability whenever > k. In the case of k = 3, it...
The preferential attachment graph Gm(n) is a random graph formed by adding a new vertex at each time step, with m edges which point to vertices selected at random with probability...