On 3-Coloring of ( 2 P 4 , C 5 )-Free Graphs.

The 3-coloring of hereditary graph classes has been a deeply-researched problem in the last decade. A hereditary graph class is characterized by a (possibly infinite) list of minimal forbidden induced subgraphs H 1 , H 2 , … ; the graphs in the class are called ( H 1 , H 2 , … ) -free. The complexity of 3-coloring is far from being understood, even for classes defined by a few small forbidden induced subgraphs. For H-free graphs, the complexity is settled for any H on up to seven vertices. There are only two unsolved cases on eight vertices, namely 2 P 4 and P 8 . For P 8 -free graphs, some partial results are known, but to the best of our knowledge, 2 P 4 -free graphs have not been explored yet. In this paper, we show that the 3-coloring problem is polynomial-time solvable on ( 2 P 4 , C 5 ) -free graphs.

Investigation of Permeation of Theophylline through Skin Using Selected Piperazine-2,5-Diones.

Transdermal administration of drugs that penetrate, in this case directly into the blood circulation, has many advantages and is promising for many drugs thanks to its easy application and good patient compliance. (S)-8-Methyl-6,9-diazaspiro[4.5]decan-7,10-dione (alaptide), has been studied as a potential chemical permeation enhancer. Based on its structure, four selected piperazine-2,5-diones were synthesized by means of multi-step synthetic pathways. All the compounds were investigated on their ability to enhance the permeation of the model drug theophylline from the hydrophilic medium propylene glycol:water (1:1). In vitro experiments were performed using vertical Franz diffusion cells at constant temperature 34 ± 0.5 °C and using full-thickness pig (Sus scrofa f. domestica) ear skin. Withdrawn samples were analyzed by RP-HPLC for determination of the permeated amount of theophylline. All the compounds were applied in ratio 1:10 (w/w) relative to the amount of theophylline. One hour after application, the permeated amount of theophylline from formulations with alaptide and (3S,6S)-3,6-dimethylpiperazine-2,5-dione, was ca. 15- and 12-fold higher, respectively, than from the formulation without the tested compounds. Despite the enhancement ratio of both enhancers in a steady state was ca. 2.3, the pseudo-enhancement ratio in the time range from 1 to 3 h was 4.4. These enhancement ratios indicate that the compounds are able to enhance the permeation of agents through the skin; however, the short-term application of both compound formulations seems to be more advantageous. In addition, the screening of the cytotoxicity of all the prepared compounds was performed using three cell lines, and the compounds did not show any significant toxic effect.

Improvement of Glibenclamide Water Solubility by Nanoparticle Preparation.

Glibenclamide, a drug used for the treatment of type 2 diabetes, belongs to Class II of Biopharmaceutical Classification System. It is a highly permeable, but poorly water-soluble drug. Nanoparticles of glibenclamide were prepared by an emulsion solvent evaporation method using dichloromethane as a solvent of glibenclamide and 3% (w/w) aqueous solution of carboxymethyl dextran sodium salt as a stabilizer, which was found as optimal. A solubility test comparing the water solubility of glibenclamide bulk and nanoparticles confirmed the improved (2-fold higher) solubility of glibenclamide nanoparticles (0.045 µg/ml) compared with bulk (0.024 µg/ml).