# Improved Approximate EFX Guarantees for Multigraphs

arXiv: https://arxiv.org/abs/2506.09288 · HTML: https://mlsanity.com/paper/2506.09288/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jun 2025.

## Built on by (most cited first, 1 of 1)

- [EFX Allocation In (Multi)Hypergraphs](https://mlsanity.com/paper/2608.03171/) (2026)

## Abstract (arXiv)

In recent years, a new line of work in fair allocation has focused on EFX allocations for ((p, q))-bounded valuations, where each good is relevant to at most (p) agents, and any pair of agents share at most (q) relevant goods. For the case (p = 2) and (q = ∞), such instances can be equivalently represented as multigraphs whose vertices are the agents and whose edges represent goods, each edge incident to exactly the one or two agents for whom the good is relevant. A recent result of citetamanatidis2024pushing shows that for additive (2,∞) bounded valuations, a ((nicefrac23))-EFX allocation always exists. In this paper, we improve this bound by proving the existence of a ((nicefrac1√2))-(efx) allocation for additive ((2,∞))-bounded valuations.