Cohen-Macaulay weighted chordal graphs
Shuai Wei
TL;DR
This paper provides a combinatorial characterization of Cohen-Macaulay weighted chordal graphs, establishing that such graphs are Cohen-Macaulay if and only if they are unmixed, thus linking algebraic properties to combinatorial structure.
Contribution
It introduces a precise combinatorial criterion for Cohen-Macaulayness in weighted chordal graphs, expanding understanding of their algebraic and combinatorial interplay.
Findings
Weighted chordal graphs are Cohen-Macaulay if and only if they are unmixed.
Provides a combinatorial characterization of Cohen-Macaulay weighted chordal graphs.
Establishes a direct link between algebraic property (Cohen-Macaulay) and combinatorial structure (unmixedness).
Abstract
In this paper I give a combinatorial characterization of all the Cohen-Macaulay weighted chordal graphs. In particular, it is shown that a weighted chordal graph is Cohen- Macaulay if and only if it is unmixed.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Graph theory and applications · Advanced Combinatorial Mathematics