On lower bounds for the matching number of subcubic graphs

We give a complete description of the set of triples (a,b,c) of real numbers with the following property. There exists a constant K such that a n_3 + b n_2

• c n_1 - K is a lower bound for the matching number of every connected subcubic graph G, where n_i denotes the number of vertices of degree i for each i.