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Regularity and Projective Dimension of Higher Independence Complex Ideals of Chordal Graphs

Closed combinatorial formulas for the Castelnuovo-Mumford regularity and projective dimension of the Stanley-Reisner ideal of the t-independence complex of a chordal graph: regularity is (t-1) times the induced matching number of the associated hypergraph and projective dimension equals the ideal's big height, characterizing linear resolutions and the Cohen-Macaulay property.

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STANLEY-REISNER IDEALS OF HIGHER INDEPENDENCE COMPLEXES OF CHORDAL GRAPHS KANOY KUMAR DAS, AMIT

For a graph G and integer t at least 2, the t-independence complex Ind_t(G) is the collection of vertex subsets whose induced subgraph has every connected component of size at most t-1; its Stanley-R…