因子臨界圖

Chapter 1 Basic Terminology and Graphic Parameters(1)
1.1Basic terminologies(1)
1.2Graphic Parameters(2)

Chapter 2 Graphic 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 3 Properties of Fractional Factor Critical Graphs(67)
3.1Fractional (f，n)-Critical Graphs(67)
3.2Fractional (g，f，n)-Critical Graphs(82)

Chapter 4 All 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 5 Fractional 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)

Graph theory is one of the branches of modern mathematics which has shown impressive advances in recent years.Graph theory is widely applied in physics，chemistry，biology，network theory，information sciences and other fields，and so it has attracted a great deal of attention. Factor theory of graph is an important branch in graph theory.

It has extensive applications in various areas，e.g.，combinatorial design，network design，circuit layout，scheduling problems，the filetransfering problems and so on.The fractional factor problem in graphs can be considered as a relaxation of the wellknown cardinality matching problem.The fractional factor problem has widerange applications in areas such as network design，scheduling and combinatorial polyhedra.For instance，in a communication network if we allow several large data packets to be sent to various destinations through several channels，the efficiency of the network will be improved if we allow the large data packets to be partitioned into small parcels.