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Simplicial Girth and Pure Resolutions

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Abstract

Generalizing the notion of the girth of a graph, a sequence of simplicial girths is assigned to each simplicial complex. Given a simplicial girth, lower bounds on higher simplicial girths are proven. When a simplicial girth is given and the Stanley–Reisner ring has a pure resolution, upper bounds on the number of vertices are proven.

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Authors and Affiliations

  1. Vanderbilt University, Nashville, USA

    Michael Goff

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  1. Michael Goff
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Correspondence to Michael Goff.

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Goff, M. Simplicial Girth and Pure Resolutions. Graphs and Combinatorics 29, 225–240 (2013). https://doi.org/10.1007/s00373-011-1113-3

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  • DOI: https://doi.org/10.1007/s00373-011-1113-3

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