Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8903593 | European Journal of Combinatorics | 2018 | 25 Pages |
Abstract
Binomial edge ideals are a noteworthy class of binomial ideals that can be associated with graphs, generalizing the ideals of 2-minors. For bipartite graphs we prove the converse of Hartshorne's Connectedness Theorem, according to which if an ideal is Cohen-Macaulay, then its dual graph is connected. This allows us to classify Cohen-Macaulay binomial edge ideals of bipartite graphs, giving an explicit and recursive construction in graph-theoretical terms. This result represents a binomial analogue of the celebrated characterization of (monomial) edge ideals of bipartite graphs due to Herzog and Hibi (2005).
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Davide Bolognini, Antonio Macchia, Francesco Strazzanti,