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arXiv · 1202.6461

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

Hsin-Hao Lai·Ko-Wei Lih
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Abstract

Let D be an acyclic orientation of the graph G. An arc of D is dependent if its reversal creates a directed cycle. Let m(G) denote the minimum number of dependent arcs over all acyclic orientations of G. For any k > 0, a generalized Mycielski graph M_k(G) of G is defined. Note that M_1(G) is the usual Mycielskian 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 underlying graph of a Hasse diagram is called a cover graph. Let c(G) denote the the minimum number of edges to be deleted from a graph G to get a cover graph. Analogue results about c(G) are also obtained.

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Hsin-Hao Lai, Ko-Wei Lih. 2012-02-29. The Minimum Number of Dependent Arcs and a Related Parameter of Generalized Mycielski Graphs. https://arxiv.org/abs/1202.6461

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