Due to an oversight by the Publisher, the following articles have appeared in Discrete Applied Mathematics without any indication that these papers were supposed to be in the Mathematical Software Section of the journal. The Publisher wishes to apologise for this oversight to the authors of the articles and also to the Mathematical Software Section editors.
In this paper we present an efficient algorithm for generating maximal triangle-free graphs. A program based on this algorithm has been used to check a conjecture of Erdo´´s about the local density of triangle-free graphs and turned out to be very powerful for the computation of triangle Ramsey numbers.
We determine the Ramsey numbers $r(K_3,G)$ for all $261080$ connected graphs of order $9$ and further Ramsey numbers of this type for some graphs of order up to $12$. Almost all of them were determined by computer programs which are based on a program for generating maximal triangle-free graphs.
Stephan Brandt合作论文数3Gunnar Brinkmann合作论文数Fakultät für Mathematik, Universität Bielefeld3
Matthias Ehrgott合作论文数Management Science, Lancaster University1
Mauricio G. C. Resende合作论文数Department of Industrial and Systems Engineering, University of Washington;Faculty of Center for Applied Optimization, University of Florida1
Panos M. Pardalos合作论文数Center for Applied Optimization, University of Florida;Department of Industrial and Systems Engineering, University of Florida1Oliver Heidemeier合作论文数1
Leonidas S. Pitsoulis合作论文数Aristotle University of Thessaloniki1
Christian Blum合作论文数Artificial Intelligence Research Institute, Spanish National Research Council1
