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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.
Bibtex entry:
| AUTHOR | = | {Kir{\'a}ly, Zolt{\'a}n and Kulkarni, Neeraja and McMeeking, Ian and Mundinger, Joshua}, |
| TITLE | = | {The Manickam-Miklós-Singhi Parameter of Graphs and Degree Sequences}, |
| NOTE | = | {{\tt www.cs.elte.hu/egres}}, |
| INSTITUTION | = | {Egerv{\'a}ry Research Group, Budapest}, |
| YEAR | = | {2018}, |
| NUMBER | = | {TR-2018-11} |