Ascending subgraph decompositions of regular graphs

Abstract

We prove that every regular graph with ((n+1)(2)) + t edges, 0 less than or equal to t < n + 1, can be decomposed into n subgraphs G(1),G(2),...,G(n) such that E(G(i)) = i and G(i) less than or equal to G(i+1) for i = 1,2,...,n - 1 and E(G(n)) = n + t. (C) 2002 Elsevier Science B.V. All rights reserved.