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Zeroes of orthogonal polynomials by QD-algorithm

Jiří Fiala — 1969

Aplikace matematiky

In the paper a method for computing zeroes of orthogonal polynomials is presented. An algorithm is given for computing directly the top row of the QD-scheme for some recurrently defined polynomials. The algorithm is then applied to classical orthogonal polynomials.

New lower bounds on the weighted chromatic number of a graph

Massimiliano CaramiaJirí Fiala — 2004

Discussiones Mathematicae Graph Theory

In this paper we present theoretical and algorithmic results for the computation of lower bounds on the chromatic number of a weighted graph. In particular, we study different ways of a possible improvement of the lower bound offered by a maximum weighted clique. Based on our findings we devise new algorithms and show their performance on random graphs.

Partial covers of graphs

Jirí FialaJan Kratochvíl — 2002

Discussiones Mathematicae Graph Theory

Given graphs G and H, a mapping f:V(G) → V(H) is a homomorphism if (f(u),f(v)) is an edge of H for every edge (u,v) of G. In this paper, we initiate the study of computational complexity of locally injective homomorphisms called partial covers of graphs. We motivate the study of partial covers by showing a correspondence to generalized (2,1)-colorings of graphs, the notion stemming from a practical problem of assigning frequencies to transmitters without interference. We compare the problems of...

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