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Transactions of the American Mathematical Society

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Associated primes of powers of edge ideals and ear decompositions of graphs


Authors: Ha Minh Lam and Ngo Viet Trung
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 13C05, 05C70, 05E40
DOI: https://doi.org/10.1090/tran/7662
Published electronically: April 25, 2019
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Abstract: In this paper, we give a complete description of the associated primes of every power of the edge ideal in terms of generalized ear decompositions of the graph. This result establishes a surprising relationship between two seemingly unrelated notions of commutative algebra and combinatorics. It covers all previous major results in this topic and has several interesting consequences.


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Additional Information

Ha Minh Lam
Affiliation: Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, 10307 Hanoi, Vietnam
Email: hmlam@math.ac.vn

Ngo Viet Trung
Affiliation: International Centre for Research and Postgraduate Training, Institute of Mathematics, Vietnam Academy of Science and Technology,18 Hoang Quoc Viet, 10307 Hanoi, Vietnam
Email: nvtrung@math.ac.vn

DOI: https://doi.org/10.1090/tran/7662
Keywords: Edge ideal, depth, associated prime, embedded prime, power of ideal, index of stability, weighted graph, matching number, matching-critical graph, factor-critical graph, non-bipartite graph, ear decomposition.
Received by editor(s): January 3, 2018
Received by editor(s) in revised form: July 12, 2018
Published electronically: April 25, 2019
Additional Notes: This work was supported by Vietnam National Foundation for Science and Technology Development under grant number 101.04-2017.19 and by Project ICRTM 01_2019.02 of the International Center for Research and Postgraduate Training in Mathematics, VAST
Article copyright: © Copyright 2019 American Mathematical Society