MIHAI TALMACIU Department of Mathematics, Informatics and Education Sciences,
Faculty of Sciences, "Vasile Alecsandri" University of Bacău,
Calea Mărăşeşti 157, Bacău 600115, ROMANIA,
e-mail: mtalmaciu@ub.ro, mihaitalmaciu@yahoo.com
Using weak decomposition, we characterize in a unified manner the classes of doubly chordal, of hereditary dually chordal and of strongly chordal graphs. We also give a recognition algorithm that is applicable for doubly chordal graphs, for hereditary dually chordal and for strongly chordal graphs. In addition, we determine the combinatorial op-timization numbers in efficient time for all the above classes of graphs.