Canadian Mathematical Bulletin· 2026Q2
Monomial ideals whose all matching powers are Cohen–Macaulay
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- Q2SCImago
- 2026year
Short summary
This paper classifies monomial ideals where all matching powers are Cohen–Macaulay, extending to edge ideals and providing an algebraic analog to Tutte's theorem on perfect matchings.
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Key points
- Identifies and classifies monomial ideals where all matching powers are Cohen–Macaulay.
- Focuses on edge ideals, characterizing the Cohen–Macaulayness of the last matching power.
- Establishes an algebraic analog to Tutte's theorem concerning graphs with perfect matchings.
- Completely solves the classification problem for chordal, very well-covered, and Cameron–Walker graphs.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract In the present article, we aim to classify monomial ideals whose all matching powers are Cohen–Macaulay. We especially focus our attention on edge ideals. The Cohen–Macaulayness of the last matching power of an edge ideal is characterized, providing an algebraic analog of the famous Tutte theorem regarding graphs having a perfect matching. For chordal graphs, very well-covered graphs, and Cameron–Walker graphs, we completely solve our problem.
The authors' abstract, as published at the source. Canadian Mathematical Bulletin, 2026 · DOI ↗
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Field: Algebra and Number Theory
Algebra and Number TheoryMathematics