Cohen–Macaulay Circulant Graphs

DOI10.1080/00927872.2012.749886zbMath1327.13077arXiv1210.8351OpenAlexW2004834330MaRDI QIDQ5412048

Adam Van Tuyl, Catriona Watt, Kevin N. Vander Meulen

Publication date: 25 April 2014

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.8351

zbMATH Keywords

circulant graphsCohen-Macaulayedge ideals

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55) Structural characterization of families of graphs (05C75) Combinatorial aspects of simplicial complexes (05E45)

Related Items (13)

A large class of graphs with a small subclass of Cohen–Macaulay members ⋮ Graded Betti numbers of some families of circulant graphs ⋮ On Gorenstein circulant graphs ⋮ Line graphs with a Cohen-Macaulay or Gorenstein clique complex ⋮ Equality of ordinary and symbolic powers of some classes of monomial ideals ⋮ On quasi-equigenerated and Freiman cover ideals of graphs ⋮ Independence Complexes of Well-Covered Circulant Graphs ⋮ On the reduced Euler characteristic of independence complexes of circulant graphs ⋮ Cohen-Macaulayness of two classes of circulant graphs ⋮ Betti numbers of some circulant graphs ⋮ Cohen-Macaulay growing graphs ⋮ Path ideals of weighted graphs ⋮ A characterization of triangle-free Gorenstein graphs and Cohen-Macaulayness of second powers of edge ideals

Cites Work

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• Splittings of independence complexes and the powers of cycles
• Well-covered circulant graphs
• Independence polynomials of circulants with an application to music
• Cohen-Macaulay graphs
• Cohen--Macaulay chordal graphs
• Distributive lattices, bipartite graphs and Alexander duality
• Circulants and their connectivities
• Decompositions of Simplicial Complexes Related to Diameters of Convex Polyhedra
• The Upper Bound Conjecture and Cohen-Macaulay Rings
• WELL-COVERED GRAPHS: A SURVEY
• Monomial Ideals

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