The sequentially Cohen–Macaulay property of edge ideals of edge-weighted graphs

Let I ( G , w ) be the edge ideal of an edge-weighted graph ( G , w ) . We prove that I ( G , w ) is sequentially Cohen–Macaulay for all weight functions w if and only if G is a Woodroofe graph.

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Bibliographic Details
Published in:Journal of algebraic combinatorics 2024-09, Vol.60 (2), p.589-597
Main Authors: Diem, Ly Thi Kieu, Minh, Nguyên Công, Vu, Thanh
Format: Article
Language:English
Subjects:
Combinatorics
Computer Science
Convex and Discrete Geometry
Group Theory and Generalizations
Lattices
Mathematics
Mathematics and Statistics
Order
Ordered Algebraic Structures
Weighting functions
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Description
Summary:Let I ( G , w ) be the edge ideal of an edge-weighted graph ( G , w ) . We prove that I ( G , w ) is sequentially Cohen–Macaulay for all weight functions w if and only if G is a Woodroofe graph.
ISSN:0925-9899
1572-9192
DOI:10.1007/s10801-024-01344-9