The Research Of Special Factors In Graph

The research in a graph with certain characteristics of the factor problem in graph theory is an important research field and also one of the most active projects in a graph theory research, Its theory is full-developing gradually and has been widely used in network design and computer science.At present, many scholars have done a great deal of research about the graph factors and problems of factorization problem and obtained fruitful achievments.The main contents: Firstly, to summarize the relevant conclusions which has been made in the general graph factor and factorization; Secondly, to discuss a sufficient condition for the existence of a path factor from the unique nature of complete graph,and to further research its conclusion,and then obtained a sufficient condition for the existence of a path factor in a K n- e graph or K n- M graph; Finally, in this paper, a neighborhood union condition for graphs to the fractional (k , n )?critical is given, and the condition is sharp in some sense.