Asymptotic Growth of Associated Primes of Certain Graph Ideals

Details Asymptotic Growth of Associated Primes of Certain Graph Ideals Asymptotic Growth of Associated Primes of Certain Graph Ideals

2012-04-15

arxiv.org/abs/1204.3315v1

Mathematics

Commutative Algebra

11 pages, 1 figure

Scientific paper

We specify a class of graphs, $H_t$, and characterize the irreducible decomposition of all powers of the cover ideals. This gives insight into the structure and stabilization of the corresponding associated primes; specifically, providing an answer to the question "For each integer $t\geq 0$, does there exist a (hyper)graph $H_t$ such that stabilization of associated primes occurs at $s\geq (\chi(H_t)-1)+t$?" asked by Francisco, H\`a, and Van Tuyl. For each $t$, $H_t$ has chromatic number 3 and associated primes that stabilize at $s=2+t$.

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