A graph G is almost 4-connected if it is simple, 3-connected, has at least ve vertices, and V (G) cannot be partitioned into three sets A;B;C in such a way that jCj = 3, jAj 2, jBj 2, and no edge of G has one end in A and the other end in B. A graph K is a subdivision of a graph G if K is obtained from G by replacing its edges by internally disjoint nonzero length paths with the same ends, call...

Woess [30] introduced a curvature notion on the set of edges planar graph, called Ψ-curvature in our paper, which is stable under duality. We study geometric and combinatorial properties for class infinite graphs with non-negative Ψ-curvature. By using discharging method, we prove that such an graph number vertices (resp. faces) degree k, except k=3,4 or 6, finite. As main result, sum at least ...

Approximation algorithms for a class of planar graph problems, including planar independent set, planar vertex cover and planar dominating set, were intensively studied. The current upper bound on the running time of the polynomial time approximation schemes (PTAS) for these planar graph problems is of 2 n. Here we study the lower bound on the running time of the PTAS for these planar graph pro...

We consider directed planar graphs with an upward planar drawing on the rolling and standing cylinders. These classes extend the upward planar graphs in the plane. Here, we address the dual graphs. Our main result is a combinatorial characterization of these sets of upward planar graphs. It basically shows that the roles of the standing and the rolling cylinders are interchanged for their duals.

Dynamic causal modeling (DCM) of functional magnetic resonance imaging (fMRI) data allows one to make inferences about the architecture of distributed networks in the brain, in terms of effective connectivity. fMRI data are usually acquired using echo planar imaging (EPI). EPI sequences typically acquire slices at different times over a few seconds. DCM, in its original inception, was not infor...

A new method is presented that enables image acquisition to be segmented into two readouts. This is achieved using a new pulse sequence that creates two components of magnetization with different spatial profiles. Each component of the magnetization is measured in one of the readouts. This produces two images with complimentary "sensitivity profiles" and near identical contrast. The images can ...

the aim of present paper is to provide mathematical modelling for the two-dimensional mhd flow with induced magnetic field. the flaws in the already existing equations have been pointed out. the results of low magnetic reynolds number approximation are recovered as a special case from the developed equations. as an example, the peristaltic flow for a couple stress fluid in a channel is consider...

river bank erosion can result in considerable riparian land loss and the delivery of large volumes of sediment to reaches downstream. consequently, the ability to predict the stability and failure geometry of eroding river banks is an important prerequisite for es-timating the rate of bank erosion and sediment yield associated with bank erosion. in this paper a new model capable of analyzing th...

This chapter deals with compressed coding of graphs. We focus on planar graphs, a widely studied class of graphs. A planar graph is a graph that admits an embedding in the plane without edge crossings. Planar maps (class of embeddings of a planar graph) are easier to study than planar graphs, but as a planar graph may admit an exponential number of maps, they give little information on graphs. ...