Perfect Matchings Avoiding Several Independent Edges in a Star‐Free Graph

In Aldred and Plummer (Discrete Math 197/198 (1999) 29–40) proved that every m‐connected ‐free graph of even order has a perfect matching M with and , where F₁ and F₂ are prescribed disjoint sets of independent edges with and . It is known that if l satisfies , then the star‐free condition in the above result is best possible. In this paper, for , we prove a refinement of the result in which the condition is replaced by the weaker condition that G is ‐free (note that the new condition does not depend on l). We also show that if m is even and either or , then for m‐connected graphs G with sufficiently large order, one can replace the condition by the still weaker condition that G is ‐free. The star‐free conditions in our results are best possible.