Lower bounds on the independence number of certain graphs of odd girth at least seven Original Research Article

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 image has an independent set of order at least image where image and image denote the order and size of image, respectively. We conjecture that every connected subcubic graph image of odd girth at least seven has an independent set of order at least image and verify our conjecture under some additional technical assumptions.