These are normalized functions regular and univalent in E: IzI < 1, for which f( E) is starlike with respect to the origin. Let y be a circle contained in E and let [ be the center of y. The Pinchuk question is this: Iff(z) is in ST, is it true thatf(y) is a closed curve that is starlike with respect tof(i)? In Section 5 we will see that the answer is no. There seems to be no reason to demand t...

In image processing and pattern recognition, the accuracy of most algorithms is dependent on a good parameterization, generally a computation scale or an estimation of the amount of noise, which may be global or variable within the input image. Recently, a simple and linear time algorithm for arc detection in images was proposed [1]. Its accuracy is dependent on the correct evaluation of the am...

A circular-arc graph is the intersection graph of arcs on a circle. A Helly circular-arc graph is a circular-arc graph admitting a model whose arcs satisfy the Helly property. A clique-independent set of a graph is a set of pairwise disjoint cliques of the graph. It is NP-hard to compute the maximum cardinality of a clique-independent set for a general graph. In the present paper, we propose po...

We establish universality limits for measures on a subarc of the unit circle. Assume that μ is a regular measure on such an arc, in the sense of Stahl, Totik, and Ullmann, and is absolutely continuous in an open arc containing some point z0 = e0 . Assume, moreover, that μ′ is positive and continuous at z0. Then universality for μ holds at z0, in the sense that the reproducing kernel Kn (z, t) f...

A circular-arc graph G is the intersection graph of a collection of arcs on the circle and such a collection is called a model of G. Say that the model is proper when no arc of the collection contains another one, it is Helly when the arcs satisfy the Helly Property, while the model is proper Helly when it is simultaneously proper and Helly. A graph admitting a Helly (resp. proper Helly) model ...

A circular-arc graph is the intersection graph of arcs of a circle. A Helly circular-arc graph is a circular-arc graph admitting a model whose arcs satisfy the Helly property. A clique-independent set of a graph is a set of pairwise disjoint cliques of the graph. It is NP-hard to compute the maximum cardinality of a clique-independent set for a general graph. In the present paper, we propose al...

We study the dominating set reconfiguration problem with token sliding rule. Let G be a graph \(G=(V,E)\) and two sets \(D_s\) \(D_t\) of G. The goal is to decide if there exists sequence \(S=\langle D_1:=D_s,\ldots ,D_{\ell }:=D_t \rangle \) such that for any consecutive \(D_r\) \(D_{r+1}\) \(r<t\), \(D_{r+1}=(D_r\setminus u) \cup \{v \}\), where \(uv\in E\).

Let x(G) and w(G) denote the chromatic number and clique number (maximum size of a clique) of a graph G. To avoid trivial cases, we always assume that w (G);?: 2. It is well known that interval graphs are perfect, in particular x( G)= w (G) for every interval graph G. In this paper we study the closeness of x and w for two well-known non-perfect relatives of interval graphs: multiple interval g...

A circular-arc graph is the intersection graph of arcs of a circle. It is a well-studied graph model with numerous natural applications. A certifying algorithm is an algorithm that outputs a certificate, along with its answer (be it positive or negative), where the certificate can be used to easily justify the given answer. While the recognition of circular-arc graphs has been known to be polyn...