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...

Full description

Saved in:
Bibliographic Details
Published inAlgorithms Vol. 17; no. 8; p. 359
Main Author Lee, Chuan-Min
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.08.2024
Subjects
Algorithms
Apexes
clique transversal function
Decomposition
distance-hereditary graph
Dynamic programming
Graph theory
Graphs
PTF-tree
twin set
Taiwan
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:1999-4893
1999-4893
DOI:10.3390/a17080359