Regularity of edge ideals of C4-free graphs via the topology of the lcm-lattice

Eran Nevo

Research output: Contribution to journalArticlepeer-review

29 Scopus citations

Abstract

We study the topology of the lcm-lattice of edge ideals and derive upper bounds on the Castelnuovo-Mumford regularity of the ideals. In this context it is natural to restrict to the family of graphs with no induced 4-cycle in their complement. Using the above method we obtain sharp upper bounds on the regularity when the complement is a chordal graph, or a cycle, or when the original graph is claw free with no induced 4-cycle in its complement. For the last family we show that the second power of the edge ideal has a linear resolution.

Original languageEnglish
Pages (from-to)491-501
Number of pages11
JournalJournal of Combinatorial Theory - Series A
Volume118
Issue number2
DOIs
StatePublished - 1 Jan 2011
Externally publishedYes

Keywords

  • Betti numbers
  • Chordal graph
  • Edge ideal
  • Lcm lattice

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