Abstract
A graph is d-orientable if its edges can be oriented so that the maximum in-degree of the resulting digraph is at most d. d-orientability is a well-studied concept with close connections to fundamental graph-theoretic notions and applications as a load balancing problem. In this paper we consider the $$d$$ -Orientable Deletion problem: given a graph $$G=(V,E)$$ , delete the minimum number of vertices to make Gd-orientable. We contribute a number of results that improve the state of the art on this problem. Specifically:
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