This book is divided into five chapters.In Chapter 1，we show basic terminologies，definitions and graphic parameters.In Chapter 2，we present some sufficient conditions for graphs to be(a,b,k)-critical graphs.In Chapter 3，we study fractional critical graphs which are the generalizations of fractional factors in graphs.In Chapter 4，we investigate all fractional(a,b,k)-critical graphs.In Chapter 5，we discuss a generalization of fractional factors，i.e.，fractional ID-factor-critical graphs from different perspectives.

Chapter 1 Basic Terminology and Graphic Parameters(1)
1.1Basic terminologies(1)
1.2Graphic Parameters(2)
Chapter 2Graphic Parameters Conditions for Factor Critical Graphs(5)
2.1Neighborhood conditions for (a，b，k)-Critical Graphs(5)
2.2Binding Numbers and (a，b，k)-Critical Graphs(32)
2.3Independence Numbers and (a，b，k)-Critical Graphs(52)
Chapter 3Properties of Fractional Factor Critical Graphs(67)
3.1Fractional (f，n)-Critical Graphs(67)
3.2Fractional (g，f，n)-Critical Graphs(82)
Chapter 4All Fractional Factor Critical Graphs(88)
4.1A Criterion for All Fractional (a，b，k)-Critical Graphs(88)
4.2Two Sufficient Conditions for All Fractional (a，b，k)-Critical Graphs(89)
Chapter 5Fractional ID-Factor Critical Graphs(99)
5.1Fractional ID-k-Factor-Critical Graphs(99)
5.2Fractional ID-［a，b］-Factor-Critical Graphs(133)
5.3Fractional ID-(g，f)-Factor-Critical Graphs(141)
References(146)