The number of excellent discrete Morse functions on graphs Original Research Article

In Nicolaescu (2008) the number of non-homologically equivalent excellent Morse functions defined on image was obtained in the differentiable setting. We carried out an analogous study in the discrete setting for some kinds of graphs, including image, in Ayala et al. (2009) . This paper completes this study, counting excellent discrete Morse functions defined on any infinite locally finite graph.