Bi-Cohen-Macaulay graphs
J\"urgen Herzog, Ahad Rahimi
TL;DR
This paper classifies bi-Cohen-Macaulay graphs, especially bipartite and chordal ones, and establishes a bijection between inseparable bi-Cohen-Macaulay graphs and trees, advancing understanding of their structure.
Contribution
It provides a complete classification of bi-Cohen-Macaulay graphs in bipartite and chordal cases and links inseparable graphs to trees.
Findings
Complete classification of bipartite bi-Cohen-Macaulay graphs
Identification of inseparable bi-Cohen-Macaulay graphs
Bijection between inseparable bi-Cohen-Macaulay graphs and trees
Abstract
In this paper we consider bi-Cohen-Macaulay graphs, and give a complete classification of such graphs in the case they are bipartite or chordal. General bi-Cohen-Macaulay graphs are classified up to separation. The inseparable bi-Cohen-Macaulay graphs are determined. We establish a bijection between the set of all trees and the set of inseparable bi-Cohen-Macaulay graphs.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Graph theory and applications · Advanced Combinatorial Mathematics