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Higher chordality: From graphs to complexes


Authors: Karim A. Adiprasito, Eran Nevo and Jose A. Samper
Journal: Proc. Amer. Math. Soc. 144 (2016), 3317-3329
MSC (2010): Primary 05Cxx, 05E45, 13F55
Published electronically: February 3, 2016
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Abstract: We generalize the fundamental graph-theoretic notion of chordality for higher dimensional simplicial complexes by putting it into a proper context within homology theory. We generalize some of the classical results of graph chordality to this generality, including the fundamental relation to the Leray property and chordality theorems of Dirac.


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Additional Information

Karim A. Adiprasito
Affiliation: School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540 – and – Einstein Institute of Mathematics, University of Jerusalem, Jerusalem, Israel
Email: adiprasito@math.huji.ac.il

Eran Nevo
Affiliation: Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel
Email: nevo@math.huji.ac.il

Jose A. Samper
Affiliation: Department of Mathematics, University of Washington at Seattle, Seattle, Washington 98105
Email: samper@math.washington.edu

DOI: https://doi.org/10.1090/proc/13002
Keywords: Simplicial complex, chordal graph, Leray property, Castelnuovo-Mumford regularity
Received by editor(s): May 13, 2015
Received by editor(s) in revised form: October 17, 2015
Published electronically: February 3, 2016
Additional Notes: The first author acknowledges support by an IPDE/EPDI postdoctoral fellowship, a Minerva postdoctoral fellowship of the Max Planck Society, and NSF Grant DMS 1128155
The research of the second author was partially supported by an ISF grant 805/11
Communicated by: Irena Peeva
Article copyright: © Copyright 2016 American Mathematical Society