Cohen-Macaulay $r$-partite graphs with minimal clique cover
  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. 
Asghar Madadi, Rashid Zaare-Nahandi
math.AC math.CO