| Abstract: | Alavi and his fellows defined the concept of ascending subgraph decomposition of a graph and conjectured that every graph with positive size has an ascending subgraph decomposition in paper 1]. Paper 2] proved that K n-R n-1 has a star ascending subgraph decomposition,here K n is the complete graph with order n and R n-1 is a subgraph of K n with size at most n-1. In paper 3],Ma Kejie and Chen Huaitang proved that K n-R n has an ascending subgraph decomposition when the size of R n is not greater than n. In this paper we will prove K n-R has an ascending subgraph decomposition when the size of R is less than 3n/2. This paper will also give the concept of comet and prove that K n-R n-1 has a comet ascending subgraph decomposition. |
