Cohen–Macaulay binomial edge ideals and accessible graphs

The cut sets of a graph are special vertices whose removal disconnects the graph. They fundamental in study binomial edge ideals, since they encode their minimal primary decomposition. We introduce class accessible graphs as with unmixed ideal and form an set system. prove that is Cohen-Macaulay we conjecture converse holds. settle for large classes graphs, including chordal traceable providing purely combinatorial description Cohen-Macaulayness. key idea proof to show both properties equivalent further condition, which call strong unmixedness.