We examine the simultaneous embedding with fixed edges problem for two planar graphs G1 and G2 with the focus on their intersection S = G1∩G2. In particular, we will present the complete set of intersection graphs S that guarantee a simultaneous embedding with fixed edges for (G1, G2). More formally, we define the subset ISEFE of all planar graphs as follows: A graph S lies in ISEFE if every pa...

We prove that the unique decomposition of connected graphs defined by Tutte is definable by formulas of Monadic Second-Order Logic. This decomposition has two levels: every connected graph is a tree of "2-connected components" called blocks ; every 2-connected graph is a tree of so-called 3-blocks. Our proof uses 2dags which are certain acyclic orientations of the considered graphs. We obtain a...

The rank-width is a graph parameter related in terms of fixed functions to cliquewidth but more tractable. Clique-width has nice algorithmic properties, but no good “minor” relation is known analogous to graph minor embedding for tree-width. In this paper, we discuss the vertex-minor relation of graphs and its connection with rank-width. We prove a relationship between vertex-minors of bipartit...

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Pentacyclic triterpenes, mainly, asiatic acid, madecassic acid, asiaticoside, and madecassoside are the active constituents of Centella asiatica. A pentacyclic triterpene enriched C. asiatica extract (PRE) was prepared and standardized to contain a total pentacyclic triterpenes not less than 65% w/w. This work was focused on determination of antiinflammatory, antioxidant, and tyrosinase inhibit...

Age-related diseases, such as osteoarthritis, Alzheimer's disease, diabetes, and cardiovascular disease, are often associated with chronic unresolved inflammation. Neutrophils play central roles in this process by releasing tissue-degenerative proteases, such as cathepsin G, as well as pro-inflammatory leukotrienes produced by the 5-lipoxygenase (5-LO) pathway. Boswellic acids (BAs) are pentacy...

Frankincense extracts and boswellic acids, biologically active pentacyclic triterpenes of frankincense, block leukotriene biosynthesis and exert potent anti-inflammatory effects. Screening for additional effects of boswellic acids on further proinflammatory pathways, we observed that acetyl-11-keto-beta-boswellic acid, an established direct, nonredox and noncompetitive 5-lipoxygenase inhibitor,...

The goal of the study was to evaluate the ability of filamentous fungi to biotransform the pentacyclic triterpene lupeol. The microbial transformations were carried out in shake flasks in different media. Experiments were also run with control flasks. Samples of each culture were taken every 24 hours, extracted with ethyl acetate, and analyzed by GC-MS. The biotransformation of lupeol by Asperg...

the plant kingdom. A variety of biological properties have been ascribed to this class of compounds including antiinflammatory, hepatoprotective, gastroprotective, anti-ulcer, anti-HIV, anti-cancer, anti-diabetic, hypolipidemic, antiatherosclerotic and immunoregulatory effects. As a part of our project aimed at drug discovery based on pharmacological interference with glucose metabolism, we hav...