You will get full credit for doing two out of three problems. You are encouraged to do all three problems.

- 8.2 (DG) (Hint: If the decision procedure says no to the entire graphm then there is not Rudrata path. If it sys yes, then we have to find a path. Delete an edge from the Graph. If the decision procedure says yes, do not include the edge, if it says no, note the edge will be in the path. Include it in the path. Do this for all edges. In the end, you will have the edges for Rudrata path - Why?)
- 8.6 a ( Hint:Since each literal appears at most once, convert this problem to 2 SAT problem - hence polynomial time, if a literal x_i appears in clause_j and complement of x_i(i.e., x_i bar) in clause_k, constaruct a new clause clause_j v clause_k bar).
- 8.6 b (Hint: Use the reduction from 3 Sat problem where each no variable occurs more than thrice or no literal occurs more than twice - Read page 265, 266 to Independant set problem - Argue about the degre of vertices)
- (Optional - But recommended) Please listen to this audio from 4:00 minute mark Manindra Agarwal (IIT Kanpur) on 2010 July P vs NP attempt (audio)