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).
Binomial edge ideals of bipartite graphs / Bolognini, D.; Macchia, A.; Strazzanti, F.. - In: EUROPEAN JOURNAL OF COMBINATORICS. - ISSN 0195-6698. - ELETTRONICO. - 70:(2018), pp. 1-25. [10.1016/j.ejc.2017.11.004]
Binomial edge ideals of bipartite graphs
Bolognini D.;
2018-01-01
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).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
