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Let D be an acyclic orientation of the graph G. An arc of D is dependent ifits reversal creates a directed cycle. Let m(G) denote the minimum number ofdependent arcs over all acyclic orientations of G. For any k > 0, a generalizedMycielski graph M_k(G) of G is defined. Note that M_1(G) is the usualMycielskian of G. We generalize results concerning m(M_1(G)) in K. L. Collins,K. Tysdal, J. Graph Theory, 46 (2004), 285-296, to m(M_k(G)). The underlyinggraph of a Hasse diagram is called a cover graph. Let c(G) denote the theminimum number of edges to be deleted from a graph G to get a cover graph.Analogue results about c(G) are also obtained.

The Minimum Number of Dependent Arcs and a Related Parameter of Generalized Mycielski Graphs