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Diamond, J.S. and A.O. Mendelzon, Cycle structure of edge labelled graphs, Discrete Applied Mathematics 45 (1993) 5 l-62. In this paper we examine the cyclic structure of graphs with edges labelled by elements of a partial order under the operation of deleting any edge whose label is less than or equal to all labels of edges of some cycle containing that edge. We show that all graphs obtained after repeating the above operation as many times as possible have similar structure with respect todoi:10.1016/0166-218x(93)90139-f fatcat:75hy57mgynfm5kurvqbzsux6fi