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 ...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.展开更多
The definition of the ascending subgraph decomposition was given by Alavi. It has been conjectured that every graph of positive size has an ascending subgraph decomposition. In this paper it is proved that the regular...The definition of the ascending subgraph decomposition was given by Alavi. It has been conjectured that every graph of positive size has an ascending subgraph decomposition. In this paper it is proved that the regular graphs under some conditions do have an ascending subgraph decomposition.展开更多
Let G be 4 graph with () edges. We say G has an Ascending Subgraph Decomposition (ASD) if the edge set of G can be partitioned into n sets generating graphs G1,G2,...,Gn such that |E(Gi)|=i (for i=1,2,...,n) and Gi is...Let G be 4 graph with () edges. We say G has an Ascending Subgraph Decomposition (ASD) if the edge set of G can be partitioned into n sets generating graphs G1,G2,...,Gn such that |E(Gi)|=i (for i=1,2,...,n) and Gi is isomorphic to a subgraph of Gi+1 for i=1,2,...,n-1.In this paper, we prove that if G is a graph with X'(G)=d and () edges, n2d-3, then G has an ASD. Moreover, we show that if G with () edges, X'(G)=d, satisfying: nd, n4,and there is a matching M of G such that Then G has a matching ASD if dk+2 or And this result is an improvment on all the relevant results about G having a matching ASD obtained before.展开更多
文摘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.
文摘The definition of the ascending subgraph decomposition was given by Alavi. It has been conjectured that every graph of positive size has an ascending subgraph decomposition. In this paper it is proved that the regular graphs under some conditions do have an ascending subgraph decomposition.
文摘Let G be 4 graph with () edges. We say G has an Ascending Subgraph Decomposition (ASD) if the edge set of G can be partitioned into n sets generating graphs G1,G2,...,Gn such that |E(Gi)|=i (for i=1,2,...,n) and Gi is isomorphic to a subgraph of Gi+1 for i=1,2,...,n-1.In this paper, we prove that if G is a graph with X'(G)=d and () edges, n2d-3, then G has an ASD. Moreover, we show that if G with () edges, X'(G)=d, satisfying: nd, n4,and there is a matching M of G such that Then G has a matching ASD if dk+2 or And this result is an improvment on all the relevant results about G having a matching ASD obtained before.
