Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Recall that a closed walk (in a undirected graph) is a cycle if its vertices are pairwise distinct.

Does there exist random constructions of bipartite graphs without cycles with high probability?

share|cite|improve this question
You might be looking for LERW and UST. – Did Jun 4 '12 at 10:29
up vote 2 down vote accepted

If a graph has no cycles then it is clearly bipartite. Moreover a graph without cycles is a forest. So what you really want is generate trees/forests?

If you're looking to generate random labeled forests/trees then this can be done efficiently using Prüfer sequences. Every such sequence chosen at random gives you a specific labeled tree.

Random non labeled forest are a bit harder to generate.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.