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.
