Some algebraic properties of hypergraphs

Emtander, Eric; Mohammadi, Fatemeh; Moradi, Somayeh

doi:10.48550/arxiv.0812.2366

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Alexander Duals Of Complements To Chordal Clutters1

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2011

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“…As mentioned in Example 4.8, there are clutters such that every subclutter contains a complete-neighborhood vertex, but that are not chordal. We can however use a similar technique to show that clutters with a complete-neighborhood vertex in every induced subclutter are vertex decomposable, improving the previous result [14,Theorem 4.3] that such clutters are shellable: Proposition 6.11. Let C be a d-uniform clutter such that every induced subclutter has a complete-neighborhood vertex.…”

Section: Alexander Duals Of Complements To Chordal Clutterssupporting

confidence: 55%

Chordal and Sequentially Cohen-Macaulay Clutters

Woodroofe¹

2011

Electron. J. Combin.

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Mathematics Subject Classifications: 05E45, 13F55, 13C14, 05C65. AbstractWe 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.

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Section: Alexander Duals Of Complements To Chordal Clutterssupporting

confidence: 55%

Chordal and Sequentially Cohen-Macaulay Clutters

Woodroofe¹

2011

Electron. J. Combin.

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Some algebraic properties of hypergraphs

Cited by 1 publication

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Chordal and Sequentially Cohen-Macaulay Clutters

Chordal and Sequentially Cohen-Macaulay Clutters

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