Study On Equimatchable K-Factor-Critical Graphs

A simple graph G is called equimatchable if all of its maximal matchings have the same size.A graph G is said to be k-fact or-critical if the removal of any set of k vertices of G results in a graph with a perfect matchingIn this paper,we start to discuss equimatchable k-factor-critical graphs,where k ? 2 is an integral number.Firstly,we show that a graph is an equimatchable 2k-factor-critical graph if and only if it is complete,where k is a positive inte-ger.Additionally,we also give some properties of equimatchable k-factor-critical graphs,where k? 3 is an odd number.Then we provide a characterization for equimatchable 3-factor-critical graphs with connectivity 3 and 4,respective-ly.Lastly,in terms of general case where k?3 is an odd number,we mainly characterize some special graph classes of equimatchable h-factor-critical graphs of connectivity k.