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@article{BPZSta,
AUTHOR = {Bigdeli, M. and Yazdan Pour, A. A. and Zaare-Nahandi, R.},
     TITLE = {Stability of Betti numbers under reduction processes: Towards chordality of clutters},
   JOURNAL = {J. Combin. Theory Ser. A},
  FJOURNAL = {Journal of Combinatorial Theory Series A},
    VOLUME = {145},
      YEAR = {2017},
     PAGES = {129--149},
MRREVIEWER = {},
}



@article{BPZDec,
AUTHOR = {Bigdeli, M. and Yazdan Pour, A. A. and Zaare-Nahandi, R.},
     TITLE = {Decomposable clutters and a generalization of Simon's conjecture},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {531},
      YEAR = {2019},
     PAGES = {102--124},
MRREVIEWER = {},
}




@incollection{Bjo,
  author       = {Bj\"orner, A.}, 
  title        = {The homology and shellability of matroids and geometric lattices},
  booktitle    = {Matroid Applications},
  publisher    = {Cambridge Univ. Press},
  year         = 1992,
  editor       = {White, N.},
  pages        = {226--283},
  address      = {Cambridge}
}




@article{BjoWac,
AUTHOR = {Bj\"orner, A. and Wachs, M.L.},
     TITLE = {Shellable nonpure complexes and posets I},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {349},
      YEAR = {1997},
     PAGES = {1299--1327},
MRREVIEWER = {},
       DOI = {}}

@article{BjoWac2,
AUTHOR = {Bj\"orner, A. and Wachs, M.L.},
     TITLE = {Shellable nonpure complexes and posets II},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {349},
      YEAR = {1997},
     PAGES = {3945--3975},
MRREVIEWER = {},
}
       
@article{BjoEri,
AUTHOR = {Bj\"orner, A. and Eriksson, K.},
     TITLE = {Extendable shellability for rank 3 matroid complexes},
   JOURNAL = {Discrete Math},
  FJOURNAL = {Discrete Math},
    VOLUME = {132},
      YEAR = {1994},
     PAGES = {373--376},
MRREVIEWER = {},
  }


@article{BruMan,
AUTHOR = {Bruggesser, H. and Mani, P.},
     TITLE = {Shellable decompositions of cells and spheres},
   JOURNAL = {Math. Scand.},
  FJOURNAL = {Mathematica Scandinavica},
    VOLUME = {29},
      YEAR = {1972},
     PAGES = {197--205},
MRREVIEWER = {},
   }


@misc{CulGurSti,
 AUTHOR = {Culbertson, J. and Guralnik, D.P. and Stiller, P.F.},
 EPRINT = {1706.04537},
 EPRINTTYPE = {arxiv},
 TITLE = {Edge-erasures and chordal graphs},
 YEAR = {2017}}


@article{CDGS,
AUTHOR = {Culbertson, J. and Dochtermann, A. and Guralnik, D.P. and Stiller, P.F.},
     TITLE = {Extendable shellability for d-dimensional complexes on d+3 vertices},
   JOURNAL = {Electron. J. Combin.},
  FJOURNAL = {Electronic Journal of Combinatorics},
    VOLUME = {27},
      YEAR = {2020},
     PAGES = {},
MRREVIEWER = {},
    }


@article{DanKle,
AUTHOR = {Danaraj, G. and Klee, V.},
     TITLE = {Which spheres are shellable?},
   JOURNAL = {Ann. Discrete Math},
  FJOURNAL = {Annals of Discrete Mathematics},
    VOLUME = {2},
      YEAR = {1978},
     PAGES = {33--52},
MRREVIEWER = {},
  }


@article{Doc,
AUTHOR = {Dochtermann, A.},
     TITLE = {Exposed circuits, linear quotients, and chordal clutters},
   JOURNAL = {J. Combin. Theory Ser. A},
  FJOURNAL = {Journal of Combinatorial Theory Series A},
    VOLUME = {177},
      YEAR = {2021},
     PAGES = {33--52},
MRREVIEWER = {},
}



@misc{GuoSheWu,
 AUTHOR = {Guo, J. and Shen, Y. and Wu, T.},
 EPRINT = {1604.05412},
 EPRINTTYPE = {arxiv},
 TITLE = {Strong shellability of simplicial complexes},
 YEAR = {2016}}


@book {Jon,
    AUTHOR = {Jonsson, Jakob},
     TITLE = {Simplicial complexes of graphs},
    SERIES = {Lecture Notes in Mathematics},
    VOLUME = {1928},
 PUBLISHER = {Springer-Verlag, Berlin},
      YEAR = {2008},
     PAGES = {xiv+378},
      ISBN = {978-3-540-75858-7},
   MRCLASS = {05C10 (05C20 05C40 05E30 06A11 55U10)},
  MRNUMBER = {2368284},


}



@article{Kah,
AUTHOR = {Kahn, J.},
     TITLE = {A problem of P. Seymour on nonbinary matroids},
   JOURNAL = {Combinatorica},
  FJOURNAL = {Combinatorica},
    VOLUME = {5},
      YEAR = {1985},
     PAGES = {319--323},
MRREVIEWER = {},
       DOI = {10.1007/BF02579246}}




@phdthesis{Kle,
  author       = {Kleinschmidt, P.}, 
  title        = {Untersuchungen zur Struktur geometrischer Zellkomplexe insbesondere zur Schalbarkeit von p.l.-Sph\"aren und p.l.-Kugeln},
  school       = {Ruhr-Universit\"at-Bohum},
  year         = {1977}
}


@article{MorTak,
AUTHOR = {Moriyama, S. and Takeuchi, F.},
     TITLE = {Incremental construction properties in dimension two -- shellability, extendable shellability, and vertex decomposability},
   JOURNAL = {Discrete Math.},
  FJOURNAL = {Discrete Mathematics},
    VOLUME = {263},
      YEAR = {2003},
     PAGES = {295--296},
MRREVIEWER = {},
}


@article{Nik,
AUTHOR = {Nikseresht, A.},
     TITLE = {Chordality of clutters with vertex decomposable dual and ascent of clutters},
   JOURNAL = {J. Combin. Theory Ser. A},
  FJOURNAL = {Journal of Combinatorial Theory Series A},
    VOLUME = {168},
      YEAR = {2019},
     PAGES = {318--337},
MRREVIEWER = {},
}


@article{ProBil,
AUTHOR = {Provan, J.S. and Billera, L.J.},
     TITLE = {Decompositions of simplicial complexes related to diameters of convex polyhedra},
   JOURNAL = {Math. Oper. Res.},
  FJOURNAL = {Mathematical Operations Research},
    VOLUME = {5},
      YEAR = {1980},
     PAGES = {576--594},
MRREVIEWER = {},
}


@article{Sim,
AUTHOR = {Simon, R. S.},
     TITLE = {Combinatorial properties of cleanness},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {167},
      YEAR = {1994},
     PAGES = {361--388},
MRREVIEWER = {},
}



@article{Tru,
AUTHOR = {Truemper, K.},
     TITLE = {Alpha-balanced graphs and matrices and GF(3)-representability of matroids},
   JOURNAL = {J. Combin. Theory Ser. B},
  FJOURNAL = {Journal of Combinatorial Theory Series B},
    VOLUME = {32},
      YEAR = {1982},
     PAGES = {112--139},
MRREVIEWER = {},
       DOI = {10.1016/0095-8956(82)90028-4}}


@article{Wac,
AUTHOR = {Wachs, M. L.},
     TITLE = {Obstructions to shellability},
   JOURNAL = {Discrete Comput. Geom.},
  FJOURNAL = {Discrete Computational Geometry},
    VOLUME = {22},
      YEAR = {1999},
     PAGES = {95--103},
MRREVIEWER = {},}


@article{Zie,
AUTHOR = {Ziegler, G. M.},
     TITLE = {Shelling Polyhedral 3-Balls and 4-Polytopes},
   JOURNAL = {Discrete Comput. Geom.},
  FJOURNAL = {Discrete Computational Geometry},
    VOLUME = {19},
      YEAR = {1998},
     PAGES = {159--174},
MRREVIEWER = {} }



@book{ZieLec,
    AUTHOR = {Ziegler, G\"{u}nter M.},
     TITLE = {Lectures on polytopes},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {152},
 PUBLISHER = {Springer-Verlag, New York},
      YEAR = {1995},
     PAGES = {x+370},
      ISBN = {},
   MRCLASS = {52Bxx},
  MRNUMBER = {1311028},
MRREVIEWER = {Margaret M. Bayer},
}


@misc{CDGO,
 AUTHOR = {Coleman, M. and Dochtermann, A. and Geist, N. and Oh, S.},
 EPRINT = {2011.12225},
 EPRINTTYPE = {arxiv},
 TITLE = {Completing and extending shellings of vertex decomposable complexes},
 YEAR = {2020}}