# Graphical Cake Cutting via Maximin Share

arXiv: https://arxiv.org/abs/2105.04755 · HTML: https://mlsanity.com/paper/2105.04755/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 May 2021.

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

- [The Complexity of Envy-Free Graph Cutting](https://mlsanity.com/paper/2312.07043/) (2023)

## Abstract (arXiv)

We study the recently introduced cake-cutting setting in which the cake is represented by an undirected graph. This generalizes the canonical interval cake and allows for modeling the division of road networks. We show that when the graph is a forest, an allocation satisfying the well-known criterion of maximin share fairness always exists. Our result holds even when separation constraints are imposed, in which case no multiplicative approximation of proportionality can be guaranteed. Furthermore, while maximin share fairness is not always achievable for general graphs, we prove that ordinal relaxations can be attained.