A graph-theoretical approach to cancelling critical elements

This work is focused on the links between Formanʼs discrete Morse theory and graph theory. More precisely, we are interested on putting the optimization of a discrete Morse function in terms of matching theory. It can be done by describing the process of cancellation of pairs of critical simplices by means of obtaining Morse matchings on the corresponding Hasse diagram with a greater number of edges using the combinatorial notion of transference.