Cohen-Macaulayness of bipartite graphs, revisited
Rashid Zaare-Nahandi
TL;DR
This paper revisits the Cohen-Macaulay property of bipartite graphs, providing new combinatorial conditions independent of vertex orderings and introducing a fast algorithm for checking this property.
Contribution
It offers order-independent combinatorial conditions for Cohen-Macaulay bipartite graphs and presents an efficient algorithm for their verification.
Findings
New combinatorial conditions equivalent to Cohen-Macaulayness.
Conditions do not depend on vertex ordering.
A fast algorithm for checking Cohen-Macaulayness.
Abstract
Cohen-Macaulayness of bipartite graphs is investigated by several mathematicians and has been characterized combinatorially. In this note, we give some different combinatorial conditions for a bipartite graph which are equal to Cohen-Macaulayness of the graphs. Conditions in the previous works are depending on an appropriate ordering on vertices of the graph. The conditions presented in this paper are not depending to any ordering. Finally, we present a fast algorithm to check Cohen-Macaulayness of a given bipartite graph.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic Geometry and Number Theory · Advanced Combinatorial Mathematics