The following statement was conjectured by Faudree, Rousseau, Schelp and Schuster: if a graph G is a non-star graph without cycles of length m 6 4 then G is a subgraph of its complement. So far the best result concerning this conjecture is that every non-star graph G without cycles of length m 6 6 is a subgraph of its complement. In this note we show that m 6 6 can be replaced by m 6 5.

We design a fast algorithm for computing the fundamental group of the complement to any knotted polygonal graph in 3-space. A polygonal graph consists of straight segments and is given by sequences of vertices along edge-paths. This polygonal model is motivated by protein backbones described in the Protein Data Bank by 3D positions of atoms. Our KGG algorithm simplifies a knotted graph and comp...

We show that given any vertex x of a k-colour-critical graph G with a connected complement, the graph G − x can be (k − 1)-coloured so that every colour class contains at least 2 vertices. This extends the well-known theorem of Gallai, that a k-colour-critical graph with a connected complement has at least 2k − 1 vertices. Our proof does not use matching theory. It is considerably shorter, conc...

A part of the immune system that improves (complements) the ability of antibodies and phagocytic cells to clear microorganisms and injured cells from an organism, attacks the pathogen's cell membrane, and encourages inflammation called complement system. It is main part of immune system. Over thirty proteins and protein pieces compose the complement system, including cell membrane receptors, an...

background and objectives: complement proteins are some of the most important plasma proteins of the innate immune system. impaired immune function is reported in subjects who are iron deficient, and there are documents that these patients are prone to infection. this study was conducted to show whether serum c3 and c4 complement change in adult nonpregnant female with iron deficient anemia or ...

The algorithm MLS (Maximal Label Search) is a graph search algorithm that generalizes the algorithms Maximum Cardinality Search (MCS), Lexicographic Breadth-First Search (LexBFS), Lexicographic Depth-First Search (LexDFS) and Maximal Neighborhood Search (MNS). On a chordal graph, MLS computes a PEO (perfect elimination ordering) of the graph. We show how the algorithm MLS can be modified to com...

In this paper we survey the behavior of various graph operations on the graph parameters clique-width and NLC-width. We give upper and lower bounds for the clique-width and NLC-width of the modi ed graphs in terms of the clique-width and NLC-width of the involved graphs. Therefor we consider the binary graph operations join, co-join, sum, di erence, products, corona, substitution, and 1-sum, an...