Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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

Let $R$ be a reflexive binary relation and $R^*$ be its reflexive transitive closure. The question is what is the equivalent condition in terms of $R$ to $R^*$ being a partial order.

Intuitively, a reflexive transitive closure adds reflexivity and transitivity to the original relation. But just because $R$ is antisymmetric doesn't mean $R^*$ is a partial order.

share|cite|improve this question
$R$ (not counting the loops) must not have any directed cycles. – Srivatsan Dec 13 '11 at 10:10
Does it have a special name? – Pteromys Dec 14 '11 at 11:52

Directed acyclic graph (often abbreviated to DAG).

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.