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Edge Ideals with Regularity No More than Three
https://doi.org/10.1142/S1005386720000644Cited by:0 (Source: Crossref)
Abstract
We prove that if G is a gap-free and chair-free simple graph, then the regularity of the edge ideal of G is no more than 3. If G is a gap-free and P4-free graph, then it is a chair-free graph; furthermore, the complement of G is chordal, and thus the regularity of G is 2.
Research supported by the Natural Science Foundation of Shanghai (No. 19ZR1424100) and the National Natural Science Foundation of China (No. 11971338).
Communicated by Zhongming Tang
2010 MSC: primary 13D02, primary 13F55, secondary 05C10
