On the Problem of Ascending SubgraphDecompositions into Matchings

Abstract:

      Alavi has given the definition of the ascending subgraph decomposition. Heconjectured that every graph of positive size has an asceuding subgraph decomposition.In this paper it is proved that a graph G of size (?)has an ascending subgraphdecomposition {G_i}, 1≤i≤n, with G_i≈iK₂ if the edge chromatic number x＇(G)≤(n + 2)/2.