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:

@techreport{egres-18-11,

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} |