MathOverflow is a question and answer site for professional mathematicians. 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

Is anything known about Lovasz Theta Function taking integral value in non-perfect graphs? In particular, does integral value of Lovasz theta always coincide with the size of largest independent set?

For instance, graph below is non-perfect, and its Lovasz theta function gives the independence number.

Its true for a few other non-perfect graphs I tried, here's a Mathematica package I used to compute it

share|cite|improve this question
up vote 4 down vote accepted

No. For some examples see When the Lovász theta-function saturates its upper bound

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.