Multigraph realizations of degree sequences: Maximization is easy, minimization is hard

Authors:
Heather Hulett;Todd G. Will;Gerhard J. Woeginger
Affiliations:
Department of Mathematics, University of Wisconsin-La Crosse, La Crosse, WI 54601, USA;Department of Mathematics, University of Wisconsin-La Crosse, La Crosse, WI 54601, USA;Department of Mathematics and Computer Science, TU Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
Venue:
Operations Research Letters
Year:
2008

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Abstract

The following minimization problem is shown to be NP-hard: Given a graphic degree sequence, find a realization of this degree sequence as loopless multigraph that minimizes the number of edges in the underlying support graph. The corresponding maximization problem is known to be solvable in polynomial time.