On lower bounds for the matching number of subcubic graphs - Haxell, P; Scott, A (Wiley, 2016)
We give a complete description of the set of triples (α, β, γ) of real numbers with the following property. There exists a constant K such that αn3 + βn2 + γn1 - K is a lower bound for the matching number v(G) of every connected subcubic graph G, where ni denotes the number of vertices of degree i for each i.