On the structure of graphs with a uniquek-factor
Petra Johann · Journal of Graph Theory · 2000
In this paper we study the structure of graphs with a unique k-factor. Our results imply a conjecture of Hendry on the maximal number m (n,k) of edges in a graph G of order n with a unique k-factor: For we prove and construct all corresponding extremal graphs. For we prove . For n = 2kl, l ∈ ℕ, this bound is sharp, and we prove that the corresponding extremal graph is unique up to isomorphism. © 2000 John Wiley & Sons, Inc. J Graph Theory 35: 227–243, 2000