Counting and Discrete Morse Theory

  • Andrew Sack University of Florida
Keywords: undergraduate research, discrete Morse theory


We examine enumerating discrete Morse functions on graphs up to equivalence by gradient vector fields and by restrictions on the codomain.  We give formulae for the number of discrete Morse functions on specific classes of graphs (line, cycle, and bouquet of circles).


Chari, M. K., & Joswig, M. (2005). Complexes of discrete Morse functions. Discrete Mathematics, 302(1-3), 39-51. doi:10.1016/j.disc.2004.07.027

Forman, R. (1998). Morse Theory for Cell Complexes. Advances in Mathematics, 134(1), 90-145. doi:10.1006/aima.1997.1650