Introduces k-neighborhood ideals NI_k(G) of graphs and studies their Castelnuovo-Mumford regularity, projective dimension, and Cohen-Macaulayness with combinatorial characterizations in the degree-vector and edge-ideal cases.
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2 Pith papers cite this work. Polarity classification is still indexing.
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math.AC 2years
2026 2representative citing papers
If the maximal homogeneous ideal is an associated prime of the tth power of the closed neighborhood ideal of G, then the diameter of G is at most 7t-8, and this bound is sharp.
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Associated primes of powers of closed neighborhood ideals and diameters of graphs
If the maximal homogeneous ideal is an associated prime of the tth power of the closed neighborhood ideal of G, then the diameter of G is at most 7t-8, and this bound is sharp.