Arithmetical rank of the edge ideals of some n-cyclic graphs with a common edge

Authors: GUANGJUN ZHU, FENG SHI, YAN GU

Abstract: In this paper, we present some lower bounds and upper bounds on the arithmetical rank of the edge ideals of some n-cyclic graphs with a common edge. For some special n-cyclic graphs with a common edge, we prove that the arithmetical rank equals the projective dimension of the corresponding quotient ring.

Keywords: Arithmetical rank, edge ideal, projective dimension, set-theoretic complete intersection

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