1 Discrete Morse Theory  
Definition 3.  
Definition 6.  
Examples  

2 Morse Matching is NP-hard  

3 Hardness of Approximating Optimal Morse Matching  
Definition 7.  

4 Approximation Algorithms for Max-Morse Matching  
A \((D+1)/(D^2+D+1)\)-factor Approximation Algorithm  

5 Conclusions