Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40320140601Cohen-Macaulay $r$-partite graphs with minimal clique cover609617518ENAsgharMadadiUniversity of ZanjanRashidZaare-NahandiInstitute for Advanced Studies in Basic SciencesJournal Article20121007In this paper, 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 there exists a cover of an $r$-partite Cohen-Macaulay graph by disjoint cliques of size $r$, then such a cover is unique.http://bims.iranjournals.ir/article_518_74456fc52a61f817f7e2e1c754c4e297.pdf