# Chore division on a graph

arXiv: https://arxiv.org/abs/1812.01856 · HTML: https://mlsanity.com/paper/1812.01856/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Dec 2018.

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

- [On Approximate MMS Allocations on Restricted Graph Classes](https://mlsanity.com/paper/2508.06343/) (2025)

## Abstract (arXiv)

The paper considers fair allocation of indivisible nondisposable items that generate disutility (chores). We assume that these items are placed in the vertices of a graph and each agent's share has to form a connected subgraph of this graph. Although a similar model has been investigated before for goods, we show that the goods and chores settings are inherently different. In particular, it is impossible to derive the solution of the chores instance from the solution of its naturally associated fair division instance. We consider three common fair division solution concepts, namely proportionality, envy-freeness and equitability, and two individual disutility aggregation functions: additive and maximum based. We show that deciding the existence of a fair allocation is hard even if the underlying graph is a path or a star. We also present some efficiently solvable special cases for these graph topologies.