# Bounding Threshold Dimension: Realizing Graphic Boolean Functions as the AND of Majority Gates

@inproceedings{Francis2022BoundingTD,
title={Bounding Threshold Dimension: Realizing Graphic Boolean Functions as the AND of Majority Gates},
author={Mathew C. Francis and Atrayee Majumder and Rogers Mathew},
booktitle={WG},
year={2022}
}
• Published in WG 24 February 2022
• Mathematics
A graph G on n vertices is a threshold graph if there exist real numbers a1, a2, . . . , an and b such that the zero-one solutions of the linear inequality n ∑ i=1 aixi ≤ b are the characteristic vectors of the cliques of G. Introduced in [Chvátal and Hammer, Annals of Discrete Mathematics, 1977], the threshold dimension of a graph G, denoted by dimTH(G), is the minimum number of threshold graphs whose intersection yields G. Given a graph G on n vertices, in line with Chvátal and Hammer, fG…

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