Dr. Rafael Heraclio Villarreal Rodríguez

Publications listed at MathSciNet.

Preprints posted at the arXiv.

Google Scholar Citations.

Publications listed at Web of Science (ResearcherID: D-7315-2013)



1. Monomial Algebras, Monographs and Textbooks in Pure and Applied Mathematics 238, Marcel Dekker, Inc., New York, 2001. Book

2. Graphs, Rings and Polyhedra, (with I. Gitler), Aportaciones Mat. Textos, 35, Soc. Mat. Mexicana, Mexico, 2011. ISBN: 978-607-02-1630-5. Book

3. Monomial Algebras, Second Edition, Monographs and Research Notes in Mathematics, Chapman and Hall/CRC, 2015.


1. Monomial Algebras and Polyhedral Geometry, in Handbook of Algebra, Vol. 3 (M. Hazewinkel Ed.), Elsevier, Amsterdam, 2003, pp. 257–314. Book Chapters

2. Edge ideals: algebraic and combinatorial properties (with S. Morey), in Progress in Commutative Algebra, Combinatorics and Homology, Vol. 1 (C. Francisco, L. C. Klingler, S. Sather-Wagstaff and J. C. Vassilev, Eds.), De Gruyter, Berlin, 2012, pp. 85-126. Book Chapters

3. Symbolic powers of monomial ideals and Cohen-Macaulay vertex-weighted digraphs (with P. Gimenez, J. Martinez-Bernal, A. Simis and C. E. Vivares), in Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics (G. M. Greuel, et.al. Eds), Springer, Cham, pp. 491-510, 2018.


  1. Ideals with sliding depth, (with J. Herzog and W. V. Vasconcelos), Nagoya Math. J. 99 (1985), 159–172.
  2. On Gorenstein ideals of codimension four, (with W. V. Vasconcelos), Proc. Amer. Math. Soc. 98 (1986), 205–210.
  3. Rees algebras and Koszul homology, J. Algebra 119 (1988), 83–104.
  4. Cohen–Macaulay graphs, Manuscripta Math. 66 (1990), 277–293.
  5. Koszul homology of Cohen–Macaulay rings with linear resolutions, (with C. Rentería), Proc. Amer. Math. Soc. 115 (1992), 51–58.
  6. Monomial algebras, Aportaciones Matemáticas, Investigación 6 (1992), 69–75.
  7. Critical binomials of monomial curves, (with A. Alcántar), Comm. Algebra 22 (1994), 3037–3052.
  8. On the ideal theory of graphs, (with A. Simis and W. V. Vasconcelos), J. Algebra, 167 (1994), 389–416.
  9. Rees algebras of edge ideals, Comm. Algebra 23 (1995), 3513–3524.
  10. A note on generators of least degree in Gorenstein ideals, (with M. Miller), Proc. Amer. Math. Soc. 124 (1996), 377–382.
  11. Normality of subrings generated by square free monomials, J. Pure & Applied Algebra 113 (1996), 91–106.
  12. Cohen–Macaulay bipartite graphs (with M. Estrada), Arch. Math. 68 (1997), 124–128.
  13. Degree bounds in monomial subrings (with W. Bruns and W. V. Vasconcelos), Illinois J. Math. 41 (1997), 341–353.
  14. The integral closure of subrings associated to graphs (with A. Simis and W. V. Vasconcelos), J. Algebra 199 (1998), 281–289.
  15. Generic Gaussian ideals (with A. Corso and W. Vasconcelos), J. Pure & Applied Algebra 125 (1998), 117-127.
  16. On the equations of the edge cone of a graph and some applications, Manuscripta Math. 97 (1998), 309–317.
  17. Rees algebras of complete bipartite graphs, Mat. Contemp. 16 (1999), 281–289.
  18. The second Betti number of an edge ideal, (with S. Eliahou), Aportaciones Matemáticas, Comunicaciones 25 (1999), 115–119.
  19. A note on affine toric varieties (with E. Reyes and L. Zárate), Linear Algebra Appl. 318 (2000), 173–179.
  20. On the normality of monomial ideals of mixed products (with G. Restuccia), Comm. Algebra 29(8) (2001), 3571–3580.
  21. On systems of binomials in the ideal of a toric variety (with S. Eliahou), Proc. Amer. Math. Soc. 130 (2002), 345–351.
  22. On the normality of Rees algebras associated to totally unimodular matrices (with V. Bonanzinga and C. Escobar), Results Math. 41, 3/4, (2002), 258–264.
  23. Gráficas con una cubierta maximal independiente y cotas para algunos invariantes (con C. Valencia), Morfismos 6(1) (2002), 57–71.
  24. Monomial ideals and the computation of multiplicities (with D. Delfino, A. Taylor, W. V. Vasconcelos and N. Weininger), in Commutative Rings Theory and Applications, Proceedings: Fez (M. Fontana et al., Eds.), Lecture Notes in Pure and Applied Math. 231, Marcel Dekker, New York, 2003, pp. 87–106. Download the PS file
  25. Constraints for the normality of monomial subrings and birationality (with A. Simis), Proc. Amer. Math. Soc. 131 (2003), 2043–2048.
  26. Canonical modules of certain edge subrings (with C. E. Valencia), European J. Combin. 24(5) (2003), 471–487.
  27. Relative volumes and minors in monomial subrings (with C. Escobar and J. Martínez-Bernal), Linear Algebra Appl. 374 (2003), 275–290.
  28. A note on the Rees algebra of a bipartite graph (with I. Gitler and C. E. Valencia), J. Pure & Applied Algebra, 201 (2005), 17-24. Download the PDF file.
  29. Normality of semigroups with some links to graph theory, Discrete Math., 302 (2005), 267-284.
  30. Blowup algebras of ideals of vertex covers of bipartite graphs (with I. Gitler and E. Reyes), Contemp. Math. 376 (2005), 273-279. Download the PS file.
  31. Complete intersections in affine monomial curves (with I. Bermejo, P. Gimenez and E. Reyes), Bol. Soc. Mat. Mexicana (3) 11 (2005), 191-203. Download the PDF file.
  32. Linear syzygies and birational combinatorics (with A. Simis), Results Math. 48 (2005), no. 3-4, 326-343. Download the PDF file.
  33. C. Escobar, R. H. Villarreal and Y. Yoshino, Torsion freeness and normality of blowup rings of monomial ideals, Commutative Algebra, Lect. Notes Pure Appl. Math. 244, Chapman & Hall/CRC, Boca Raton, FL, 2006, pp. 69-84. Download the PS file.
  34. Explicit representations of the edge cone of a graph (with C. E. Valencia), International Journal of Contemporary Mathematical Sciences, Vol. 1, 2006, no. 1-4, 53 - 66. Download the PDF file.
  35. A note on Rees algebras and the MFMC property (with I. Gitler and C. Valencia), Beiträge Algebra Geom. 48 (2007), No. 1, 141-150. Download the PDF file.
  36. Ring graphs and toric ideals, (with I. Gitler and E. Reyes), Electronic Notes in Discrete Mathematics 28C (2007), 393-400.
  37. Unmixed bipartite graphs, Rev. Colombiana Mat. 41(2)(2007), 393-395.
  38. Normalization of monomial ideals and Hilbert functions, Proc. Amer. Math. Soc. 136 (2008), 1933-1943.
  39. Rees algebras and polyhedral cones of ideals of vertex covers of perfect graphs, J. Algebraic Combin. 27(3) (2008), 293-305.
  40. Shellable graphs and sequentially Cohen-Macaulay bipartite graphs (with A. Van Tuyl), J. Combin. Theory Ser. A 115 (2008), no.5, 799-814.
  41. Rees cones and monomial rings of matroids, Linear Algebra Appl. 428 (2008), 2933-2940.
  42. Cohen-Macaulay, Shellable and unmixed clutters with a perfect matching of Koenig type (with S. Morey and E. Reyes), J. Pure Appl. Algebra 212(7) (2008), 1770-1786.
  43. Duality, a-invariants and canonical modules of rings arising from linear optimization problems (with J. P. Brennan and L. A. Dupont), Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 51 (2008), no. 4, 279-305.
  44. Blowup algebras of square-free monomial ideals and some links to combinatorial optimization problems (with I. Gitler and E. Reyes), Rocky Mountain J. Math. 39 (2009), no. 1, 71-102. Download the PDF file.
  45. Cohen-Macaulay admissible clutters (with H. T. Ha and S. Morey), J. Commut. Algebra 1 (2009), no. 3, 463-480. Download the PDF file.
  46. Cohen-Macaulay clutters with combinatorial optimization properties and parallelizations of normal edge ideals (with L. A. Dupont and E. Reyes), Sao Paulo J. Math. Sci. 3 (2009), no. 1, 61-75. Download the PDF file.
  47. Ring graphs and complete intersection toric ideals (with I. Gitler and E. Reyes), Discrete Math. 310 (2010), no. 3, 430-441. Download the PDF file.
  48. Edge ideals of clique clutters of comparability graphs and the normality of monomial ideals (with L. A. Dupont), Math. Scand. 106 (2010), no. 1, 88-98. Download the PDF file.
  49. Ehrhart clutters: regularity and max-flow min-cut (with J. Martinez-Bernal and E. O'Shea), Electron. J. Combin. 17 (2010), no. 1, R52. Download the PDF file.
  50. Systems with the integer rounding property in normal monomial subrings (with C. Renteria and L. A. Dupont), An. Acad. Brasil. Cienc 82 (2010), no. 4, 801-811.
  51. Symbolic Rees algebras, vertex covers and irreducible representations of Rees cones (with L. A. Dupont), Algebra Discrete Math. 10 (2010), no. 2, 64-86.
  52. Algebraic methods for parameterized codes and invariants of vanishing ideals over finite fields (with C. Renteria and A. Simis), Finite Fields Appl. 17 (2011), no. 1, 81-104.
  53. Algebraic and combinatorial properties of ideals and algebras of uniform clutters of TDI systems (with L. A. Dupont), J. Comb. Optim. 21 (2011), no. 3, 269-292.
  54. Combinatorics of symbolic Rees algebras of edge ideals of clutters (with J. Martinez-Bernal, C. Renteria), Contemp. Math. 555 (2011), 151-164.
  55. The minimum distance of parameterized codes on projective tori (with E. Sarmiento and M. Vaz Pinto), Appl. Algebra Engrg. Comm. Comput. 22 (2011), no. 4, 249-264.
  56. Algebra conmutativa y codigos evaluacion (with C. Renteria), Aportaciones Matematicas, Comunicaciones 42 (2011), 171-184.
  57. Métodos algebraicos para códigos parametrizados por monomios (con E. Sarmiento, C. Renteria, A. Simis y M. Vaz Pinto), EMALCA 2010, Revista de Ciencias Basicas UJAT 9 (2011), no. 2, 17-28. Download PDF
  58. Combinatorics of Cremona monomial maps (with A. Simis), Math. Comp. 81 (2012), no. 279, 1857-1867.
  59. Toric ideals generated by circuits (with J. Martinez-Bernal), Algebra Colloq. 19 (2012), no. 4, 665-672.
  60. On the vanishing ideal of an algebraic toric set and its parameterized linear codes (with E. Sarmiento and M. Vaz Pinto), J. Algebra Appl. 11 (2012), no. 4, 1250072 (16 pages). Abstract
  61. Associated primes of powers of edge ideals (with Martinez-Bernal and S. Morey), Collect. Math. 63 (2012), no. 3, 361--374. Abstract
  62. Parameterized affine codes (with H. H. Lopez, E. Sarmiento, M. Vaz Pinto), Studia Sci. Math. Hungar. 49 (2012), no. 3, 406-418. Abstract
  63. Complete intersection vanishing ideals on degenerate tori over finite fields (with H. H. Lopez and L. Zarate), Arab. J. Math. (Springer) 2 (2013), no. 2, 189-197. Abstract
  64. Complete intersections in binomial and lattice ideals (with H. H. Lopez), Internat. J. Algebra Comput. 23 (2013), no. 6, 1419-1429. Abstract
  65. The degree and regularity of vanishing ideals of algebraic toric sets over finite fields (with M. Vaz Pinto), Comm. Algebra 41 (2013), no. 9, 3376-3396. Abstract
  66. Affine cartesian codes (H. H. Lopez and C. Renteria), Des. Codes Cryptogr. 71 (2014), no. 1, 5-19.
  67. Degree and algebraic properties of lattice and matrix ideals (with L. O'Carroll and F. Planas-Vilanova), SIAM J. Discrete Math. 28 (2014), no. 1, 394-427.
  68. Computing the degree of a lattice ideal of dimension one (with H. H. Lopez), J. Symbolic Comput. 65 (2014), 15-28.
  69. Regularity and algebraic properties of certain lattice ideals (with J. Neves and M. Vaz Pinto), Bull. Braz. Math. Soc. (N.S.) 45 (2014), no. 4, 1-30.
  70. Vanishing ideals over graphs and even cycles (with J. Neves and M. Vaz Pinto), Comm. Algebra 43 (2015), no. 3, 1050-1075.
  71. Binomial vanishing ideals (with A. Tochimani), J. Algebra Comb. Discrete Struct. Appl. 2 (2015), no. 2, 151-156.
  72. Direct products in projective Segre codes (with A. Tochimani and M. Vaz Pinto), Finite Fields Appl. 39 (2016), 96-110.
  73. On complete monomial ideals (with P. Gimenez, A. Simis and W. V. Vasconcelos), J. Commut. Algebra 8 (2016), no. 2, 207-226.
  74. Minimum distance functions of graded ideals and Reed-Muller-type codes (with J. Martinez-Bernal and Y. Pitones), J. Pure Appl. Algebra 221 (2017), 251-275.
  75. The second generalized Hamming weight of some evaluation codes arising from a projective torus (with M. González-Sarabia, E. Camps and E. Sarmiento), Finite Fields Appl. 52 (2018), 370-394.
  76. Footprint and minimum distance functions (with L. Nuñez-Betancourt and Y. Pitones), Commun. Korean Math. Soc. 33 (2018), no. 1, 85-101.
  77. Complete intersection vanishing ideals on sets of clutter type over finite fields (with A. Tochimani), Bull. Malays. Math. Sci. Soc. 41 (2018), no. 1, 81-89.
  78. Generalized minimum distance functions (with M. Gonzalez-Sarabia, J. Martinez-Bernal and C. E. Vivares), J. Algebraic Combin. 50 (2019), no. 3, 317-346.
  79. Indices of normalization of ideals (with C. Polini, B. Ulrich and W. V. Vasconcelos), J. Pure Appl. Algebra 223 (2019), no. 9, 3681-3694.
  80. Vanishing ideals over finite fields (with A. Tochimani), Math. Notes 105 (2019), no. 3, 429-438.
  81. Depth and regularity of monomial ideals via polarization and combinatorial optimization (with J. Martinez-Bernal, S. Morey and C. E. Vivares), Acta Math. Vietnam. 44 (2019), no. 1, 243-268.
  82. Edge ideals of oriented graphs (with H. T. Ha, K.-N. Lin, S. Morey, E. Reyes and R. H. Villarreal), Internat. J. Algebra Comput. 29 (2019), no. 3, 535-559.
  83. The dual of a constacyclic code, self dual, reversible constacyclic codes and constacyclic codes with complementary duals over finite local Frobenius non-chain rings with nilpotency index 3 (with C. A. Castillo-Guillen, C. Renteria, E. Sarmiento and H. Tapia-Recillas), Discrete Math. 342 (2019), no. 8, 2283-2296.
  84. Regularity of the vanishing ideal over a parallel composition of paths (with A. Macchia, J. Neves and M. Vaz Pinto), J. Commut. Algebra 12 (2020), no. 3, 391-407.
  85. Generalized minimum distance functions and algebraic invariants of Geramita ideals (with S. M. Cooper, A. Seceleanu, S. O. Tohaneanu and M. Vaz Pinto), Adv. in Appl. Math. 112 (2020), 101940.
  86. On the generalized Hamming weights of certain Reed-Muller-type codes (with D. Jaramillo and M. Gonzalez-Sarabia), Analele Univ. Ovidius din Constanta, Math. Series 28(1) (2020), 205-217.
  87. Generalized Hamming weights of projective Reed--Muller-type codes over graphs (with M. A. Valencia-Bucio and J. Martinez-Bernal), Discrete Math. 343 (2020), no. 1, 111639.
  88. Linear codes over signed graphs, (with M. A. Valencia-Bucio and J. Martinez-Bernal), Des. Codes Cryptogr. 88 (2020), 273-296.
  89. Joins, Ears and Castelnuovo-Mumford regularity, (with J. Neves and M. Vaz Pinto), J. Algebra 560 (2020), 67-88.