We study the clique problem on partite graphs. As a special type of clique, cliques on k-partite graphs have extensive applications in areas such as gene data analysis, data classification, protein function determination, recommendation systems, and social network analysis. However, existing research has largely focused on the maximum clique problem on k-partite graphs, neglecting other commonly occurring clique structures. To address this gap, for the first time, we define three special clique structures on k-partite graphs and analyze their interrelationships. We also formulate the clique enumeration problem on k-partite graphs and perform a comprehensive complexity analysis. Furthermore, we propose an efficient clique enumeration algorithm that takes advantage of the unique properties of cliques on k-partite graphs and integrates various techniques, such as pruning strategies and ordered sets, to accelerate the enumeration process. Experimental results on four real-world k-partite graphs validate the efficiency of the proposed algorithm and the effectiveness of the techniques employed.
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