Associated primes of monomial ideals and odd holes in graphs

Abstract

Let G be a finite simple graph with edge ideal I (G). Let I (G)∨ denote the Alexander dual of I (G). We show that a description of all induced cycles of odd length in G is encoded in the associated primes of (I (G)∨)2. This result forms the basis for a method to detect odd induced cycles of a graph via ideal operations, e.g., intersections, products and… (More)

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