Heckman and Thomas [C.C. Heckman, R. Thomas, A new proof of the independence ratio of triangle-free cubic graphs, Discrete Math. 233 (2001) 233–237] proved that every connected subcubic triangle-free graph G has an independent set of order at least (4n(G) − m(G) − 1)/7 where n(G) and m(G) denote the order and size of G, respectively. We conjecture that… (More)