Minimally k-factor-critical graphs.
Odile Favaron, Minyong Shi · 1998
A graph G of order n is k-factor-critical, where k is an integer of the same parity as n with 0::; k::; n, if G- X has a perfect matching for any set X of k vertices of G. A k-factor-critical graph G is called minimal if for any edge e E E(G), G- e is not k-factor-critical. In this paper we study some properties of minimally k-factor-critical graphs, in particular a bound on the minimum degree, and characterize (n- 4)and minimally (n- 4)-factor-critical graphs. 1.