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Down-left
graphs and a connection to toric ideals of graphs
Jennifer Biermann, Beth Anne Castellano, Marcella Manivel, Eden Petruccelli and Adam Van Tuyl |
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Vol. 18 (2025), No. 3, 437–458
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Abstract |
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We introduce a family of graphs, which we call down-left graphs, and study their combinatorial and algebraic properties. We show that members of this family are well-covered, -free, and vertex decomposable. By applying a result of Hà and Woodroofe, and Moradi and Khosh-Ahang, the (Castelnuovo–Mumford) regularity of the associated edge ideals is the induced matching number of the graph. As an application, we give a combinatorial interpretation for the regularity of the toric ideals of chordal bipartite graphs that are -free. |
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Keywords
edge ideals, regularity, vertex decomposable, toric ideals
of graphs
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Mathematical Subject Classification
Primary: 13F55
Secondary: 13D02, 14M25
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Milestones
Received: 27 April 2023
Revised: 16 February 2024
Accepted: 18 February 2024
Published: 28 April 2025
Communicated by Jim Haglund
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Authors |
| Jennifer Biermann | |
| Department of Mathematics and
Computer Science Hobart and William Smith Colleges Geneva, NY United States |
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| Beth Anne Castellano | |
| Department of Mathematics Dartmouth College Hanover, NH United States |
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| Marcella Manivel | |
| Department of Mathematics University of Minnesota Minneapolis, MN United States |
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| Eden Petruccelli | |
| Department of Mathematics and
Statistics McMaster University Hamilton, ON Canada |
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| Adam Van Tuyl | |
| Department of Mathematics and
Statistics McMaster University Hamilton, ON Canada |
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| © 2025 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). |
