We say that a simple graphG is induced matching extendable, shortly IM-extendable, if every induced matching of G is included in a perfect matching of G. The main results of this paper are as follows: (1) For every connected IM-extendable graph G with |V (G)| ≥ 4, the girth g(G) ≤ 4. (2) If G is a connected IM-extendable graph, then |E(G)| ≥ 2 |V (G)| − 2; the equality holds if and only if G ∼= T ×K2, where T is a tree. (3) The only 3-regular connected IM-extendable graphs are Cn × K2, for n… CONTINUE READING