Forbidden Induced Subgraphs for Perfect Matchings.

Let $${\mathcal{F}}$$ be a family of connected graphs. A graph G is said to be $${\mathcal{F}}$$-free if G is H-free for every graph H in $${\mathcal{F}}$$. We study the problem of characterizing the families of graphs $${\mathcal{F}}$$ such that every large enough connected $${\mathcal{F}}$$-free graph of even order has a perfect matching. This problems was previously studied in Plummer and Saito (J Graph Theory 50(1):1-12, ), Fujita et al. (J Combin Theory Ser B 96(3):315-324, ) and Ota et al. (J Graph Theory, 67(3):250-259, ), where the authors were able to characterize such graph families $${\mathcal{F}}$$ restricted to the cases $${|\mathcal{F}|\leq 1, |\mathcal{F}| \leq 2}$$ and $${|\mathcal{F}| \leq 3}$$, respectively. In this paper, we complete the characterization of all the families that satisfy the above mentioned property. Additionally, we show the families that one gets when adding the condition $${|\mathcal{F}| \leq k}$$ for some k ≥ 4. [ABSTRACT FROM AUTHOR]