A circle graph is the intersection graph of a family of chords on a circle. There is no known characterization of circle graphs by forbidden induced subgraphs that do not involve the notions of local equivalence or pivoting operations. We characterize circle graphs by a list of minimal forbidden induced subgraphs when the graph belongs to one of the following classes: linear domino graphs, P4-t...

A circle graph is the intersection graph of chords drawn in a circle. The best known general upper bound on the chromatic number of circle graphs with clique number k is 50 · 2. We prove a stronger bound of 2k − 1 for graphs in a simpler subclass of circle graphs, so called clean graphs. Based on this result we prove that the chromatic number of every circle graph with clique number at most 3 i...

The main purpose of this paper is to consider an explicit form of the Padé-type operators. To do so, we consider the representation of Padétype approximants to the Fourier series of the harmonic functions in the open disk and of the L-functions on the circle by means of integral formulas, and, then we define the corresponding Padé-type operators. We are also concerned with the properties of the...