Critical extreme points of the 2-edge connected spanning subgraph polytope

In this paper we study the extreme points of the polytope P(G), the linear relaxation of the 2-edge connected spanning subgraph polytope of a graph G. We introduce a partial ordering on the extreme points of P(G) and give necessary conditions for a non-integer extreme point of P(G) to be minimal with respect to that ordering. We show that, if is a non-integer minimal extreme point of P(G), then G and can be reduced, by means of some reduction operations, to a graph G' and an extreme point of P(G') where G' and satisfy some simple properties. As a consequence we obtain a characterization of the perfectly 2-edge connected graphs, the graphs for which the polytope P(G) is integral. Received: May, 2004 Part of this work has been done while the first author was visiting the Research Institute for Discrete Mathematics, University of Bonn, Germany.     

Tunisian Native Mentha pulegium L. Extracts: Phytochemical Composition and Biological Activities

Mint species (Lamiaceae family) have been used as traditional remedies for the treatment of several diseases. In this work, we aimed to characterize the biological activities of the total phenolic and flavonoid contents of Mentha pulegium L. extracts collected from two different regions of Tunisia. The highest amounts of total phenols (74.45 ± 0.01 mg GAE/g DW), flavonoids (28.87 ± 0.02 mg RE/g DW), and condensed tannins (4.35 ± 0.02 mg CE/g DW) were found in the Bizerte locality. Methanolic leaf extracts were subjected to HPLC-UV analysis in order to identify and quantify the phenolic composition. This technique allowed us to identify seven phenolic compounds: two phenolic acids and five flavonoid compounds, such as eriocitrin, hesperidin, narirutin, luteolin, and isorhoifolin, which were found in both extracts with significant differences between samples collected from the different regions (p < 0.05). Furthermore, our results showed that the methanolic extract from leaves collected from Bizerte had the highest antioxidant activities (DPPH IC₅₀ value of 16.31 μg/mL and 570.08 μmol Fe²⁺/g, respectively). Both extracts showed high radical-scavenging activity as well as significant antimicrobial activity against eight tested bacteria. The highest antimicrobial activities were observed against Gram-positive bacteria with inhibition zone diameters and MIC values ranging between 19 and 32 mm and 40 and 160 µg/mL, respectively. Interestingly, at 10 μg/mL, the extract had a significant effect on cell proliferation of U87 human glioblastoma cells. These findings open perspectives for the use of Mentha pulegium L. extract in green pharmacy, alternative/complementary medicine, and natural preventive therapies for the development of effective antioxidant, antibacterial, and/or antitumoral drugs.