Cohen-Macaulay graphs with large girth
D\^o Trong Hoang, Nguy\^en Cong Minh, and Tr\^an Nam Trung
TL;DR
This paper classifies Cohen-Macaulay graphs with large girth and planar Gorenstein graphs, showing they are also vertex decomposable, thus advancing understanding of their algebraic and combinatorial properties.
Contribution
It provides a classification of Cohen-Macaulay graphs with girth at least 5 and planar Gorenstein graphs with girth at least 4, establishing their vertex decomposability.
Findings
Cohen-Macaulay graphs with girth ≥ 5 are classified.
Planar Gorenstein graphs with girth ≥ 4 are characterized.
Such graphs are proven to be vertex decomposable.
Abstract
We classify Cohen-Macaulay graphs of girth at least and planar Gorenstein graphs of girth at least . Moreover, such graphs are also vertex decomposable.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Advanced Combinatorial Mathematics · Algebraic Geometry and Number Theory