(K₃+e)-Decomposition Of Dense Graphs

The graph decomposition of dense graph has been concerned by many scholars at home and abroad..From the 20th century,Wilson obtain the basic theorem:for any given F,any sufficiently large F-divisible clique G can be partitioned into copies of F,that is when the F degree is n-1 existence F-decomposition.This article is based on the point degree condition of r-regular graph decomposition in the dense graph of Barber et al,considering the point condition of the decomposition of the irregular graph by the vertices of n sufficiently large (?)-divisible graph G,and getting the optimal minimum degree is ?(G)? 3/4n + o(n),existing (?)-decomposition((?)graph is(K3 + e)).The structure of this article is as follows:In the first chapter,the research background and current situation of dense graph decomposition are briefly introduced,and the related concepts are given and the main results of this paper are briefly described.In the second chapter,constructional graph F-absorber and find the condition of F-absorber in graph G and the size of its degree of degeneracy.In the third chapter,we prove that graph G is approximate decomposition under the condition of the existence of F-absorber in graph G,which proves that graph G has F-decomposition.In the fourth chapter,expanding the promotion,research in the graph (?) to see the edge,and a necessary condition for the existence of the optimal decomposition conjecture the lower bound.