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Given an undirected graph, each of the two end-vertices of an edge can ownthe edge. Call a vertex poor, if it owns at most one edge. We give a polynomialtime algorithm for the problem of finding an assignment of owners to the edgeswhich minimizes the number of poor vertices. In the terminology of graphorientation, this means finding an orientation for the edges of a graphminimizing the number of edges with out-degree at most 1, and answers aquestion of Asahiro Jansson, Miyano, Ono (2014).

On finding orientations with fewest number of vartices with small out-degree