8 citations · 18 across the 4 of their papers we have counts for
4 papers
Cohen-Macaulay Polymatroidal Ideals
Juergen Herzog, Takayuki Hibi
All Cohen--Macaulay polymatroidal ideals are classified. The Cohen--Macaulay polymatroidal ideals are precisely the principal ideals, the Veronese ideals, and the squarefree Verone…
Cohen-Macaulay chordal graphs
Juergen Herzog, Takayuki Hibi, Xinxian Zheng
We classify all Cohen-Macaulay chordal graphs. In particular. it is shown that a chordal graph is Cohen-Macaulay if and only if its unmixed.
Level rings arising from meet-distributive meet-semilattices
Juergen Herzog, Takayuki Hibi
The Alexander dual of an arbitrary meet-semilattice is described explicitly. Meet-distributive meet-semilattices whose Alexander dual is level are characterized.
Dirac's theorem on chordal graphs and Alexander duality
Jürgen Herzog, Takayuki Hibi, Xinxian Zheng
By using Alexander duality on simplicial complexes we give a new and algebraic proof of Dirac's theorem on chordal graphs.