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A very well-covered graph is a well-covered graph without isolated vertices such that the height of its edge ideal is half of the number of vertices. In this survey article, we gather together most of the old and new results on the edge and cover ideals of these graphs.
Research in the Mathematical Sciences – Springer Journals
Published: Jun 1, 2022
Keywords: Betti number; CMt\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{CM}_t$$\end{document} property; Cohen–Macaulay graph; Cohen–Macaulay ring; Compression; Cover ideal; Depth; Edge ideal; Edge-weighted ideal; Flag complex; f-Vector; Height; h-Vector; Independence complex; Linear resolution; Local cohomology; Minimal free resolution; Projective dimension; Regularity; Shellability; Simplicial complex; Stanley–Reisner ideal; Symbolic power; Vertex-decomposability; Very well-covered graph; Well-covered graph; 05C75; 05C90; 13D45; 13F55; 13H10; 55U10
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