On the relationship between the genus and the cardinality of the maximum matchings of a graph

Lower bounds on the cardinality of the maximum matchings of graphs are established in terms of a linear polynomial of p, p⁽¹⁾, p⁽²⁾ and γ whose coefficients are functions of κ, where p is the number of the vertices of a graph, p⁽ⁱ⁾ the number of the vertices of degree i (i = 1,2), γ the genus and κ the connectivity.