The Manickam-Mikl\'os-Singhi Parameter of Graphs and Degree Sequences
Combinatorics
2018-08-20 v1
Abstract
Let be a simple graph. Consider all weightings of the vertices of with real numbers whose total sum is nonnegative. How many edges of 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.
Keywords
Cite
@article{arxiv.1808.05835,
title = {The Manickam-Mikl\'os-Singhi Parameter of Graphs and Degree Sequences},
author = {Zoltán Király and Neeraja Kulkarni and Ian McMeeking and Joshua Mundinger},
journal= {arXiv preprint arXiv:1808.05835},
year = {2018}
}