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
A conjecture concerning a new kind of subgraph decomposition, the ascendingsubgraph decomposition, was proposed by Alavi Y. et al., as follows: Every graph ofpositive size has an ascending subgraph decomposition. In t...A conjecture concerning a new kind of subgraph decomposition, the ascendingsubgraph decomposition, was proposed by Alavi Y. et al., as follows: Every graph ofpositive size has an ascending subgraph decomposition. In this paper it is proved thatG = Kn- H2n-1 has an ascending subgraph decomposition, where H2n-1 is any graphwith at most n venices and at most 2n - 1 edges (n > 6).展开更多
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.
文摘A conjecture concerning a new kind of subgraph decomposition, the ascendingsubgraph decomposition, was proposed by Alavi Y. et al., as follows: Every graph ofpositive size has an ascending subgraph decomposition. In this paper it is proved thatG = Kn- H2n-1 has an ascending subgraph decomposition, where H2n-1 is any graphwith at most n venices and at most 2n - 1 edges (n > 6).
