EdgeIdeals: a package for (hyper)graphs An edge ideal is a square-free monomial ideal where the generators of the monomial ideal correspond to the edges of the (hyper)graph. An edge ideal complements the Stanley-Reisner correspondence (see SimplicialComplexes) by providing an alternative combinatorial interpretation of the monomial generators. This package exploits the correspondence between square-free monomial ideals and the combinatorial objects, by using commutative algebra routines to derive information about (hyper)graphs. For some of the mathematical background on this material, see Chapter 6 of the textbook Monomial Algebras by R. Villarreal and the survey paper of T. Ha and A. Van Tuyl (”Resolutions of square-free monomial ideals via facet ideals: a survey,” Contemporary Mathematics. 448 (2007) 91-117).
Keywords for this software
References in zbMATH (referenced in 8 articles , 1 standard article )
Showing results 1 to 8 of 8.
- Selvaraja, S.: Symbolic powers of vertex cover ideals (2020)
- Baker, Jonathan; Vander Meulen, Kevin N.; Van Tuyl, Adam: Shedding vertices of vertex decomposable well-covered graphs (2018)
- Moore, W. Frank; Rogers, Mark; Sather-Wagstaff, Sean: Monomial ideals and their decompositions (2018)
- Kubik, Bethany; Sather-Wagstaff, Sean: Path ideals of weighted graphs (2015)
- Van Tuyl, Adam: Edge ideals using Macaulay2 (2013)
- Francisco, Christopher A.; Hà, Huy Tài; Van Tuyl, Adam: Colorings of hypergraphs, perfect graphs, and associated primes of powers of monomial ideals (2011)
- Francisco, Christopher A.; Hà, Huy Tài; Van Tuyl, Adam: Associated primes of monomial ideals and odd holes in graphs (2010)
- Francisco, Christopher A.; Hoefel, Andrew; Van Tuyl, Adam: EdgeIdeals: a package for (hyper)graphs (2009)