Geodesic
Chordal and sequentially Cohen-Macaulay clutters
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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We extend the definition of chordal from graphs to clutters. The resulting family generalizes both chordal graphs and matroids, and obeys many of the same algebraic and geometric properties. Specifically, the independence complex of a chordal clutter is shellable, hence sequentially Cohen-Macaulay; and the circuit ideal of a certain complement to such a clutter has a linear resolution. Minimal non-chordal clutters are also closely related to obstructions to shellability, and we give some general families of such obstructions, together with a classification by computation of all obstructions to shellability on 6 vertices.
DOI : 10.37236/695
Classification : 05E45, 13F55, 13C14, 05C65
Mots-clés : Minimal non-chordal clutters, shellability 
@article{10_37236_695,
     author = {Russ Woodroofe},
     title = {Chordal and sequentially {Cohen-Macaulay} clutters},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/695},
     zbl = {1236.05213},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/695/}
}
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Russ Woodroofe. Chordal and sequentially Cohen-Macaulay clutters. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/695

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