Author:
Bolognini Davide,Macchia Antonio,Strazzanti Francesco
Abstract
AbstractThe cut sets of a graph are special sets of vertices whose removal disconnects the graph. They are fundamental in the study of binomial edge ideals, since they encode their minimal primary decomposition. We introduce the class of accessible graphs as the graphs with unmixed binomial edge ideal and whose cut sets form an accessible set system. We prove that the graphs whose binomial edge ideal is Cohen–Macaulay are accessible and we conjecture that the converse holds. We settle the conjecture for large classes of graphs, including chordal and traceable graphs, providing a purely combinatorial description of Cohen–Macaulayness. The key idea in the proof is to show that both properties are equivalent to a further combinatorial condition, which we call strong unmixedness.
Funder
Istituto Nazionale di Alta Matematica “Francesco Severi”
Einstein Stiftung Berlin
Deutsche Forschungsgemeinschaft
Publisher
Springer Science and Business Media LLC
Subject
Discrete Mathematics and Combinatorics,Algebra and Number Theory
Cited by
8 articles.
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