Algebraic Methods for Detecting Odd Holes in a Graph
نویسنده
چکیده
Let G denote a finite simple graph with edge ideal I(G). Letting I(G) denote the Alexander dual of I(G), we show that a description of the induced cycles of G of odd length is encoded in the associated primes of (I(G)). This result forms the basis for an algorithm to detect all the odd induced cycles of a graph via ideal operations, e.g., intersections, products, and colon operations. Moreover, we get simple algebraic algorithms for determining whether a graph is perfect. We also show how to determine the existence of odd induced cycles in a graph from the value of the arithmetic degree or the regularity of (I(G)).
منابع مشابه
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