Computational complexity of classical problems for hereditary clique-helly graphs

• Main Authors: Flavia Bonomo, Guillermo Durán
• Format: Article
• Language: English
• Published: Sociedade Brasileira de Pesquisa Operacional 2004-12-01
• Series: Pesquisa Operacional
• Subjects: computational complexity; hereditary clique-Helly graphs; split graphs
• Online Access: http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382004000300006

A graph is clique-Helly when its cliques satisfy the Helly property. A graph is hereditary clique-Helly when every induced subgraph of it is clique-Helly. The decision problems associated to the stability, chromatic, clique and clique-covering numbers are NP-complete for clique-Helly graphs. In this note, we analyze the complexity of these problems for hereditary clique-Helly graphs. Some of them can be deduced easily by known results. We prove that the clique-covering problem remains NP-complete for hereditary clique-Helly graphs. Furthermore, the decision problems associated to the clique-transversal and the clique-independence numbers are analyzed too. We prove that they remain NP-complete for a smaller class: hereditary clique-Helly split graphs.