A glimpse to most of the old and new results on very well-covered graphs from the viewpoint of commutative algebra

K. Kimura, M. R. Pournaki, S. A. Seyed Fakhari, N. Terai, S. Yassemi

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Article number29
JournalResearch in Mathematical Sciences
Volume9
Issue number2
DOIs
Publication statusPublished - Jun 2022

Keywords

  • Betti number
  • CM property
  • Cohen–Macaulay graph
  • Cohen–Macaulay ring
  • Compression
  • Cover ideal
  • Depth
  • Edge ideal
  • Edge-weighted ideal
  • f-Vector
  • Flag complex
  • h-Vector
  • Height
  • 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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Mathematics (miscellaneous)
  • Computational Mathematics
  • Applied Mathematics

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