# On weak majority dimensions of digraphs

## TL;DR

This paper introduces the concept of weak majority dimension for digraphs, characterizes those with dimensions 0 and 1, and explores properties and specific cases like paths and cycles.

## Contribution

It defines the weak majority dimension for any digraph, characterizes low-dimensional cases, and establishes that digraphs with dimension at most two are transitive.

## Key findings

- Weak majority dimension can be arbitrarily large.
- Complete characterization of digraphs with dimension 0 and 1.
- Directed paths and cycles' dimensions are computed.

## Abstract

In this paper, we introduce the notion of the weak majority dimension of a digraph which is well-defined for any digraph. We first study properties shared by the weak dimension of a digraph and show that a weak majority dimension of a digraph can be arbitrarily large. Then we present a complete characterization of digraphs of weak majority dimension $0$ and $1$, respectively, and show that every digraph with weak majority dimension at most two is transitive. Finally, we compute the weak majority dimensions of directed paths and directed cycles and pose open problems.