Cohen-Macaulay r-partite graphs with minimal clique cover
classification
🧮 math.AC
math.CO
keywords
cohen-macaulaygraphpartitecliquecoversomecliquesconditions
read the original abstract
In this note, we give some necessary conditions for an $r$-partite graph such that the edge ring of the graph is Cohen-Macaulay. It is proved that if $G$ is an $r$-partite Cohen-Macaulay graph which is covered by some disjoint cliques of size $r$, then the clique cover is unique.
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