Notes on Factor-Criticality, Extendibility and Independence Number

Abstract

In this paper, we give a sufficient and necessary condition for a \(k\)-extendable graph to be \(2k\)-factor-critical when \(k = \frac{v}{4}\), and prove some results on independence numbers in \(n\)-factor-critical graphs and \(k\frac{1}{2}\)-extendable graphs.