Pushing vertices in digraphs without long induced cycles
Discrete Applied Mathematics
Neighborhood unions and cyclability of graphs
Discrete Applied Mathematics
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In this paper we introduce a new hamiltonian-like property of graphs. A graph G is said to be cyclable if for each orientation D of G there is a set S of vertices such that reversing all the arcs of D with one end in S results in a hamiltonian digraph. We characterize cyclable complete multipartite graphs and prove that the fourth power of any connected graph G with at least five vertices is cyclable. If, moreover, G is two-connected then its cube is cyclable. These results are shown to be best possible in a sense. © 1998 John Wiley & Sons, Inc. J Graph Theory 28: 13–30, 1998