# Unmixed $r$-partite graphs

Document Type: Research Paper

Authors

1 Department of Mathematics‎, ‎Institute for Advanced Studies‎ ‎in Basic Science (IASBS)‎, ‎P.O‎. ‎Box 45195-1159‎, ‎Zanjan‎, ‎Iran.

2 Department of Mathematics‎, ‎Institute for Advanced Studies‎ ‎in Basic Science (IASBS)‎, ‎P.O‎. ‎Box 45195-1159‎, ‎Zanjan‎, ‎Iran.}

Abstract

‎Unmixed bipartite graphs have been characterized by Ravindra and‎ ‎Villarreal independently‎. ‎Our aim in this paper is to‎ ‎characterize unmixed $r$-partite graphs under a certain condition‎, ‎which is a generalization of Villarreal's theorem on bipartite‎ ‎graphs‎. ‎Also, we give some examples and counterexamples in relevance to this subject‎.

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### History

• Receive Date: 28 November 2015
• Revise Date: 19 February 2016
• Accept Date: 19 February 2016