|Title:||Maximum induced multicliques and complete multipartite subgraphs in polygon-circle graphs and circle graphs
|Abstract:||This is a Revised Version of CS-2011-04. A graph is a multiclique if its connected components are cliques. A graph is a complete multipartite graph if its vertex set has a partition into independent sets such that every two vertices in different independent sets are adjacent. A graph is a multiclique-multipartite graph if its vertex set has a partition U, W such that G(U) is complete multipartite, G(W) is a multiclique and every two vertices uU, vW are adjacent. We describe a polynomial time algorithm to find maximum induced complete multipartite subgraphs in polygon-circle graphs. We describe polynomial time algorithms to find maximum induced multicliques and multiclique-multipartite subgraphs in circle graphs. These problems have applications for clustering of proteins by PPI criteria, of documents, and of web pages.|
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