Research Paper#Graph Theory, Parameterized Complexity, Fair Division🔬 ResearchAnalyzed: Jan 3, 2026 06:13
Parameterized Complexity of Fair Orientations in Graphs
Published:Dec 31, 2025 18:30
•1 min read
•ArXiv
Analysis
This paper investigates the computational complexity of finding fair orientations in graphs, a problem relevant to fair division scenarios. It focuses on EF (envy-free) orientations, which have been less studied than EFX orientations. The paper's significance lies in its parameterized complexity analysis, identifying tractable cases, hardness results, and parameterizations for both simple graphs and multigraphs. It also provides insights into the relationship between EF and EFX orientations, answering an open question and improving upon existing work. The study of charity in the orientation setting further extends the paper's contribution.
Key Takeaways
- •Introduces the study of EF orientations in graphs.
- •Applies parameterized complexity analysis to identify tractable and intractable cases.
- •Provides results for both simple graphs and multigraphs.
- •Answers an open question regarding the structural parameterized complexity of EFX orientations.
- •Considers charity in the orientation setting, establishing algorithms for finding the minimum amount of edges to remove for EF(X) orientations to exist.
Reference
“The paper initiates the study of EF orientations, mostly under the lens of parameterized complexity, presenting various tractable cases, hardness results, and parameterizations.”