We describe a polynomial time algorithm to find a minimum feedback vertex set, or equivalently, a maximum induced forest, in a circle graph. The circle graphs are the overlap graphs of intervals on a line.

We prove Diestel’s conjecture that the square G of a 2-connected locally finite graph G has a Hamilton circle, a homeomorphic copy of the complex unit circle S in the Freudenthal compactification of G.

Outerstring graphs are the intersection graphs of curves that lie inside a disk such that each curve intersects the boundary of the disk. Outerstring graphs are among the most general classes of intersection graphs studied. To date, no polynomial time algorithm is known for any of the classical graph optimization problems on outerstring graphs; in fact, most are NP-hard. It is known that there ...

Outerstring graphs are the intersection graphs of curves that lie inside a disk such that each curve intersects the boundary of the disk in one of its endpoints. Outerstring graphs were introduced in 1991 and are amongst the most general classes of intersection graphs studied, including among others, chordal graphs and interval filament graphs. To date no polynomial time algorithm is known for ...

An algebraic distance graph is defined to be a graph with vertices in En in which two vertices are adjacent if and only if the distance between them is an algebraic number. It is proved that an algebraic distance graph with finite vertex set is complete if and only if the graph is "rigid". Applying this result, we prove that ( 1 ) if all the sides of a convex polygon T which is inscribed in a c...

the hermeneutic circle articulated by different hermeneuticans in various versions is one of the basic problems in modern hermeneutics. romanic hermeneutics introduced the circle as a methodological principle, but in philosophical hermeneutics the circle has ontological dimensions and regards as a process of understanding. heidegger believes that hermeneutic circle reflects dasein’s existential...

For a set P of points in the plane, we introduce a class of triangulations that is an extension of the Delaunay triangulation. Instead of requiring that for each triangle the circle through its vertices contains no points of P inside, we require that at most k points are inside the circle. Since there are many different higher-order Delaunay triangulations for a point set, other useful criteria...

A graph is a multiclique if its connected components are cliques. A graph is a complete multipartite graph if its vertex set has a partition into independent sets such that every two vertices in different independent sets are adjacent. The complement of a graph G is denoted coG. A graph is a multiclique-multipartite graph if its vertex set has a partition U, W such that G(U) is complete multipa...