# Cohen-Macaulay $r$-partite graphs with minimal clique cover

Document Type : Research Paper

Authors

1 University of Zanjan

2 Institute for Advanced Studies in Basic Sciences

Abstract

‎In 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.

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### History

• Receive Date: 07 October 2012
• Revise Date: 19 April 2013
• Accept Date: 19 April 2013