Multigraph realizations of degree sequences: Maximization is easy, minimization is hard
Operations Research Letters
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We view a loopless multigraph as a complete graph with nonnegative integer edge weights indicating the multiplicity of each edge. A multigraph realization of a given degree sequence is parsimonious if it has the least number of positive weight edges. We characterize the graphs that can appear as components in a parsimonious multigraph and show that minimizing the number of positive weight edges is equivalent to maximizing the number of cycle-free components.