Lower bounds on the cardinality of the maximum matchings of planar graphs

AbstractLower bounds on the cardinality of the maximum matchings of planar graphs, with a constraint on the minimum degree, are established in terms of a linear polynomial of the number of vertices. The bounds depend upon the minimum degree and the connectivity of graphs. Some examples are given which show that all the lower bounds are best possible in the sense that neither the coefficients nor the constant terms can be improved