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arXiv · 1808.05835

The Manickam-Mikl\'os-Singhi Parameter of Graphs and Degree Sequences

Zoltán Király·Neeraja Kulkarni·Ian McMeeking·Joshua Mundinger
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Abstract

Let $G$ be a simple graph. Consider all weightings of the vertices of $G$ with real numbers whose total sum is nonnegative. How many edges of $G$ have endpoints with a nonnegative sum? We consider the minimum number of such edges over all such weightings as a graph parameter. Computing this parameter has been shown to be NP-hard but we give a polynomial algorithm to compute the minimum of this parameter over realizations of a given degree sequence. We also completely determine the minimum and maximum value of this parameter for regular graphs.

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Zoltán Király, Neeraja Kulkarni, Ian McMeeking, Joshua Mundinger. 2018-08-17. The Manickam-Mikl\'os-Singhi Parameter of Graphs and Degree Sequences. https://arxiv.org/abs/1808.05835

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