Packing triangles in low degree graphs and indifference graphs

We consider the problems of finding the maximum number of vertex-disjoint triangles (VTP) and edge-disjoint triangles (ETP) in a simple graph. Both problems are NP-hard. The algorithm with the best approximation ratio known so far for these problems has ratio 3/2 + epsilon, a result that follows from a more general algorithm for set packing obtained by Hurkens and Schrijver [On the size of systems of sets every t of which have an SDR, with an application to the worst-case ratio of heuristics for packing problems, SIAM J. Discrete Math. 2(1) (1989) 68-72]. We present improvements on the approximation ratio for restricted cases of VTP and ETP that are known to be APX-hard: we give an approximation algorithm for VTP on graphs with maximum degree 4 with ratio slightly less than 1.2, and for ETP on graphs with maximum degree 5 with ratio 4/3. We also present an exact linear-time algorithm for VTP on the class of indifference graphs. (C) 2007 Elsevier B.V. All rights reserved.

Designing Novel Antitrypanosomal Agents from a Mixed Graph-Theoretical Substructural Approach

Chagas disease is nowadays the most serious parasitic health problem. This disease is caused by Trypanosoma cruzi. The great number of deaths and the insufficient effectiveness of drugs against this parasite have alarmed the scientific community worldwide. In an attempt to overcome this problem, a model for the design and prediction of new antitrypanosomal agents was obtained. This used a mixed approach, containing simple descriptors based on fragments and topological substructural molecular design descriptors. A data set was made up of 188 compounds, 99 of them characterized an antitrypanosomal activity and 88 compounds that belong to other pharmaceutical categories. The model showed sensitivity, specificity and accuracy values above 85%. Quantitative fragmental contributions were also calculated. Then, and to confirm the quality of the model, 15 structures of molecules tested as antitrypanosomal compounds (that we did not include in this study) were predicted, taking into account the information on the abovementioned calculated fragmental contributions. The model showed an accuracy of 100% which means that the ""in silico"" methodology developed by our team is promising for the rational design of new antitrypanosomal drugs. (C) 2009 Wiley Periodicals, Inc. J Comput Chem 31: 882-894. 2010

Design of novel antituberculosis compounds using graph-theoretical and substructural approaches

The increasing resistance of Mycobacterium tuberculosis to the existing drugs has alarmed the worldwide scientific community. In an attempt to overcome this problem, two models for the design and prediction of new antituberculosis agents were obtained. The first used a mixed approach, containing descriptors based on fragments and the topological substructural molecular design approach (TOPS-MODE) descriptors. The other model used a combination of two-dimensional (2D) and three-dimensional (3D) descriptors. A data set of 167 compounds with great structural variability, 72 of them antituberculosis agents and 95 compounds belonging to other pharmaceutical categories, was analyzed. The first model showed sensitivity, specificity, and accuracy values above 80% and the second one showed values higher than 75% for these statistical indices. Subsequently, 12 structures of imidazoles not included in this study were designed, taking into account the two models. In both cases accuracy was 100%, showing that the methodology in silico developed by us is promising for the rational design of antituberculosis drugs.