Abstract
A graph G with positive integral node-weights b i is said to be a b-König-Egerváry graph (b-KEG for short) if there exist a transversal T and a b-matching λ such that the weight of T is equal to the value of λ; the usual König-Egerváry graphs correspond to b=(1, 1, …, 1).
Several characterizations and two polynomial recognition algorithms for b-KEGs are presented. Algorithm 1 either recognizes (G, b) as being a b-KEG, or else exhibits an ‘obstruction’. Algorithm 2 associates a quadratic boolean function f with (G, b) and reduces the problem of recognizing whether (G, b) is a b-KEG to that of solving the equation f=0. In case (G, b) is a b-KEG, both algorithms provide a minimum weight transversal.
Some of our results generalize previous results obtained in the unweighted case by Deming, Gavril and Sterboul.
A companion paper will analyze applications of the weighted König-Egerváry property to quadratic 0–1 optimization.
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© 1984 The Mathematical Programming Society, Inc.
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Bourjolly, J.M., Hammer, P.L., Simeone, B. (1984). Node-weighted graphs having the König-Egerváry property. In: Korte, B., Ritter, K. (eds) Mathematical Programming at Oberwolfach II. Mathematical Programming Studies, vol 22. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0121007
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DOI: https://doi.org/10.1007/BFb0121007
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