Chromatic Bounds from Edge Ideal Syzygies
Research Paper#Graph Theory, Algebraic Geometry, Combinatorics🔬 Research|Analyzed: Jan 4, 2026 00:04•
Published: Dec 25, 2025 22:30
•1 min read
•ArXivAnalysis
This paper explores the relationship between the chromatic number of a graph and the algebraic properties of its edge ideal, specifically focusing on the vanishing of syzygies. It establishes polynomial bounds on the chromatic number based on the vanishing of certain Betti numbers, offering improvements over existing combinatorial results and providing efficient coloring algorithms. The work bridges graph theory and algebraic geometry, offering new insights into graph coloring problems.
Key Takeaways
- •Establishes polynomial bounds on the chromatic number based on the vanishing of syzygies in the edge ideal.
- •Improves upon existing combinatorial results, such as Wagon's result on $(i+1)K_2$-free graphs.
- •Provides efficient coloring algorithms with O(n^3) time complexity.
- •Connects graph theory and algebraic geometry to provide new insights into graph coloring.
Reference / Citation
View Original"The paper proves that $χ\leq f(ω),$ where $f$ is a polynomial of degree $2j-2i-4.$"