Generating random regular graphs

Random regular graphs play a central role in combinatorics and theoretical computer science. In this paper, we analyze a simple algorithm introduced by Steger and Wormald [10] and prove that it produces an asymptotically uniform random regular graph in a polynomial time. Precisely, for fixed d and n with d = O(n1/3), it is shown that the algorithm generates an asymptotically uniform random d-regular graph on n vertices in time O(nd2 ). This confirms a conjecture of Wormald. The key ingredient in the proof is a recently developed concentration inequality by the second author. The algorithm works for relatively large d in practical (quadratic) time and can be used to derive many properties of uniform random regular graphs.

• Type: Conference
• Year: 2003
• Where: STOC
• Authors: Jeong Han Kim, Van H. Vu
• Keywords: Algorithms, Random D-regular Graph, Random Regular Graphs, Simple Algorithm, STOC 2003