Toric ideals of matching polytopes and edge colorings
Abstract
Abstract In this paper, we investigate the maximal degree of minimal generators of the toric ideal of the matching polytope of a graph. It is known that the toric ideal associated with a bipartite graph is generated by binomials of degree at most 3. We show that this fact is equivalent to a result in the theory of edge colorings of bipartite multigraphs. Moreover, a characterization of bipartite graphs whose toric ideals are generated by quadratic binomials is given. Finally, we discuss the maximal degree of minimal generators of the toric ideal associated with a general graph and give a conjecture.
Fields of Study & Subjects
Commutative Algebra and Its Applications
Polynomial and algebraic computation
Graph Labeling and Dimension Problems
Publication details
- Journal / source
- Mathematika
- Volume
- 72
- Issue
- 2
- Publication date
- 1 April 2026
- Language
- EN