Exploring Clique Transversal Variants on Distance-Hereditary Graphs: Computational Insights and Algorithmic Approaches

The clique transversal problem is a critical concept in graph theory, focused on identifying a minimum subset of vertices that intersects all maximal cliques in a graph. This problem and its variations—such as the k-fold clique, k-clique, minus clique, and signed clique transversal problems—have received significant interest due to their theoretical importance and practical applications. This paper examines the k-fold clique, k-clique, minus clique, and signed clique transversal problems on distance-hereditary graphs. Known for their distinctive structural properties, distance hereditary graphs provide an ideal framework for studying these problem variants. By exploring these issues in the context of distance-hereditary graphs, this research enhances the understanding of the computational challenges and the potential for developing efficient algorithms to address these problems.