From the theory of an electric network containing any combination of resistances and a single variable impedance element having a constant phase angle independent of frequency, it is shown that the graph of the terminal series reactance against the resistance is an arc of a circle with the position of the center depending upon the phase angle of the variable element. If it be assumed that biolo...

A graph G is a circular-arc graph if it is the intersection graph of a set of arcs on a circle. That is, there is one arc for each vertex of G, and two vertices are adjacent in G if and only if the corresponding arcs intersect. We give a linear-time algorithm for recognizing this class of graphs. When G is a member of the class, the algorithm gives a certificate in the form of a set of arcs tha...

In the process of compiling a computer programme, we consider the problem of allocating variables to registers within a loop. It can be formulated as a coloring problem in a circular arc graph (intersection graph of a family F of intervals on a circle). We consider the meeting graph of F introduced by Eisenbeis, Lelait and Marmol. Proceedings of the Fifth Workshop on Compilers for Parallel Comp...

paper presents a new method that is capable of extracting circles from complicated and heavily corrupted images, which is not based on the Hough transform (HT). The proposed method consists of three parts. First, we approximately detect short straight lines from the image by using a fast line extraction algorithm. Second, it uses a least squares fitting algorithm for arc segments. The arc segme...

In this paper, Ultra High Energy Cosmic Ray (UHECR) data observed by the HiRes fluorescence detector in stereo mode is analyzed to search for events in the sky with an arrival direction lying on a great circle. Such a structure is known as an arc structure. An arc structure is expected when the charged cosmic rays pass through the galactic magnetic field. The arcs searched for could represent a...

A k-dimensional box is the cartesian product R1 ×R2 × · · · ×Rk where each Ri is a closed interval on the real line. The boxicity of a graph G, denoted as box(G), is the minimum integer k such that G can be represented as the intersection graph of a collection of k-dimensional boxes: that is two vertices are adjacent if and only if their corresponding boxes intersect. A circular arc graph is a ...

A circular-arc graph is the intersection graph of a family of arcs on a circle. A characterization by forbidden induced subgraphs for this class of graphs is not known, and in this work we present a partial result in this direction. We characterize circular-arc graphs by a list of minimal forbidden induced subgraphs when the graph belongs to any of the following classes: P4-free graphs, paw-fre...

The present study examined the performance of two groups of amnesic subjects on a cross-modal identification task. It was found that subjects with Korsakoff's disease did not differ from alcoholic controls on their ability to match the tactile feel of an arc with the visual appearance of the full circle from which the arc was taken. The postencephalitic subjects were, however, impaired on this ...

In many areas of human practice, one needs to approximate a set of points P1, . . . , Pn ∈ R representing experimental data or observations by a simple geometric shape, such as a line, plane, circular arc, elliptic arc, and spherical surface. This problem is known as fitting amodel object line, circle, sphere, etc. to observed data points. The best fit is achieved when the geometric distances f...

Golumbic, Lipshteyn and Stern proved that every graph can be represented as the edge intersection graph of paths on a grid, i.e., one can associate to each vertex of E-mail addresses: [email protected]; [email protected]; [email protected]; [email protected]; [email protected]; [email protected]; [email protected]. This work was partially supported by MathAmSud...