Matching extensions with prescribed and forbidden edges.
Matthew Porteous, Robert E. L. Aldred · 1996
Suppose G connected graph on p vertices that contains perfect Then G is said to have property n) if p 2: 2(m + n + 1) and if for each pair of disjoint independent M, N E ( G) of m, n there exists a perfect matching P in G such that M S;;;; P and 0. We discuss the circumstances under which E(m, n) =? E(x, y), and prove that (surprisingly) in general E(m, n) does not imply E(m, n-1). 1