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arXiv · 2610.41810

Degree Realization with Maximum Matching

Amotz Bar-Noy·Igor Kalinichev·David Peleg·Dror Rawitz
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Abstract

The Maximum Matching Degree Realization problem requires, for a sequence $d$ of $n$ positive integers, to compute a realizing graph(whose degree sequence corresponds to $d$) with the maximum possible matching. We present a polynomial-time algorithm for this problem. The decision version of this problem requires to determine whether a sequence $d$ admits a realization with a matching of size $ν$ (without computing such a realization). Recently, it was shown that it can be done by verifying a series of inequalities. We improve the existing characterization by reducing the number of inequalities.

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BibTeXRIS

Amotz Bar-Noy, Igor Kalinichev, David Peleg, Dror Rawitz. 2026-10-30. Degree Realization with Maximum Matching. https://arxiv.org/abs/2610.41810

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