2025/01/31 by Mori, Kenta, Motomura, Ryo, Ohsugi, Hidefumi +1
#05C15 #13F65 #13P10 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2501.19209
In the present 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 to 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 to a general graph and give a conjecture.