Castelnuovo-Mumford Regularity of Graphs

M. Adamaszek: Splittings of independence complexes and the powers of cycles, Journal of Combinatorial Theory Series A 119 (2012), 1031–1047.MathSciNetCrossRefzbMATHGoogle Scholar

D. Attali, A. Lieutier and D. Salinas: Efficient data structure for representing and simplifying simplicial complexes in high dimensions, International Journal of Computational Geometry and Applications 22 (2012), 279–303.MathSciNetCrossRefzbMATHGoogle Scholar

T. Biyikoğlu and Y. Civan: Four-cycled graphs with topological applications, Annals of Combinatorics 16 (2012), 37–56.MathSciNetCrossRefzbMATHGoogle Scholar

T. Biyikoğlu and Y. Civan: Bounding Castelnuovo-Mumford regularity of graphs via Lozin’s operations, unpublished manuscript, available at arXiv:1302.3064, 2013.Google Scholar

T. Biyikoğlu and Y. Civan: Vertex-decomposable graphs, codismantlability, Cohen-Macaulayness, and Castelnuovo-Mumford regularity, Electronic Journal of Combinatorics, 21(1):#P1, 2014.Google Scholar

T. Biyikoğlu and Y. Civan: Castelnuovo-Mumford regularity of graphs, available at arXiv:1503.06018(v1), 43pp, 2015.zbMATHGoogle Scholar

A. Brandstädt, V. B. Le and J. P. Spinrad: Graph Classes, A Survey, SIAM Monographs on Discrete Mathematics and Applications, Philadelphia, 1999.CrossRefGoogle Scholar

P. Csorba: Subdivision yields Alexander duality on independence complexes, Electronic Journal of Combinatorics, 16(2):#R11, 2009.Google Scholar

H. Dao, C. Huneke and J. Schweig: Bounds on the regularity and projective dimension of ideals associated to graphs, Journal of Algebraic Combinatorics 38 (2013), 37–55.MathSciNetCrossRefzbMATHGoogle Scholar

R. Ehrenborg and G. Hetyei: The topology of the independence complex, European Journal of Combinatorics 27 (2006), 906–923.MathSciNetCrossRefzbMATHGoogle Scholar

A. Engström: Complexes of directed trees and independence complexes, Discrete Mathematics 309 (2009), 3299–3309.MathSciNetCrossRefzbMATHGoogle Scholar

A. Hatcher: Algebraic Topology, Cambridge University Press, New York, 2006.zbMATHGoogle Scholar

H. T. Hà: Regularity of squarefree monomial ideals, in: S. M. Cooper and S. Sather Wagstaff, editors, Connections Between Algebra, Combinatorics, and Geometry, volume 76, 251–276. Springer, Proceedings in Mathematics and Statistics, 2014.CrossRefGoogle Scholar

H. T. Hà and A. V. Tuyl: Monomial ideals, edge ideals of hypergraphs, and their graded betti numbers, Journal of Algebraic Combinatorics 27 (2008), 215–245.MathSciNetCrossRefzbMATHGoogle Scholar

T. Januszkiewicz and J. Świątkowski: Hyperbolic Coxeter groups of large dimension, Commentarii Mathematici Helvetici 78 (2003), 555–583.MathSciNetCrossRefzbMATHGoogle Scholar

G. Kalai and R. Meshulam: Intersection of Leray complexes and regularity of monomial ideals, Journal of Combinatorial Theory Series A 113 (2006), 1586–1592.MathSciNetCrossRefzbMATHGoogle Scholar

M. Katzman: Characteristic-independence of Betti numbers of graph ideals, Journal of Combinatorial Theory Series A 113 (2006), 435–454.MathSciNetCrossRefzbMATHGoogle Scholar

D. Kozlov: Combinatorial Algebraic Topology, volume ACM 21, Springer, Berlin, 2008.CrossRefzbMATHGoogle Scholar

V. V. Lozin: On maximum induced matchings in bipartite graphs, Information Processing Letters 81 (2002), 7–11.MathSciNetCrossRefzbMATHGoogle Scholar

F. H. Lutz and E. Nevo: Stellar theory for flag complexes, Mathematica Scandinavica 118 (2016), 70–82.MathSciNetCrossRefzbMATHGoogle Scholar

M. Mahmoudi, A. Mousivand, M. Crupi, G. Rinaldo, N. Terai and S. Yassemi: Vertex decomposability and regularity of very well-covered graphs, Journal of Pure and Applied Algebra 215 (2011), 2473–2480.MathSciNetCrossRefzbMATHGoogle Scholar

M. Marietti and D. Testa: A uniform approach to complexes arising from forests, Electronic Journal of Combinatorics, 15:#R101, 2008.Google Scholar

D. Maruőič and T. Pisanski: The remarkable generalized Petersen graph G(8; 3), Mathematica Slovaca 50 (2000), 117–121.MathSciNetGoogle Scholar

S. Morey and R. H. Villarreal: Edge ideals: algebraic and combinatorial properties, in: C. Francisco, L. C. Klingler, S. Sather-Wagstaff, and J. C. Vassilev, editors, Progress in Commutative Algebra 1: Combinatorics and Homology, chapter 3, 85–126. De Gruyter, Berlin, 2012.Google Scholar

E. Nevo: Regularity of edge ideals of C4-free graphs via the topology of the lcmlattice, Journal of Combinatorial Theory Series A 118 (2011), 491–501.MathSciNetCrossRefzbMATHGoogle Scholar

E. Nevo and I. Peeva: C4-free edge ideals, Journal of Algebraic Combinatorics 37 (2013), 243–248.CrossRefzbMATHGoogle Scholar

D. Osajda: A construction of hyperbolic Coxeter groups, Commentarii Mathematici Helvetici 88 (2013), 353–367.MathSciNetCrossRefzbMATHGoogle Scholar

P. Przytycki and J. Świątkowski: Flag-no-square triangulations and Gromov boundaries in dimension 3, Groups, Geometry, and Dynamics 3 (2013), 453–468.Google Scholar

R. P. Stanley: Combinatorics and Commutative Algebra, Second Edition, volume 41, Progress in Mathematics, Birkhäuser, Boston, MA, 1996.zbMATHGoogle Scholar

W. A. Stein et al: Sage Mathematics Software, The Sage Development Team, http://www.sagemath.org, 2014.Google Scholar

A. V. Tuyl: Sequentially Cohen-Macaulay bipartite graphs: vertex decomposability and regularity, Archiv der Mathematik 93 (2009), 451–459.MathSciNetCrossRefzbMATHGoogle Scholar

D. W. Walkup: The lower bound conjecture for 3 and 4-manifolds, Acta Mathematica 125 (1970), 75–107.MathSciNetCrossRefzbMATHGoogle Scholar

G. Weetman: A construction of locally homogeneous graphs, Journal of the London Mathematical Society 50 (1994), 68–86.MathSciNetCrossRefzbMATHGoogle Scholar

G. Whieldon: Jump sequences of ideals, preprint, available at arXiv:1012.0108v1, 27pp, 2015.Google Scholar

R. Woodroofe: Matchings, coverings, and Castelnuovo-Mumford regularity, Journal of Commutative Algebra 6 (2014), 287–304.MathSciNetCrossRefzbMATHGoogle Scholar