Exoo, Geoffrey Some applications of \(pq\)-groups in graph theory. (English) Zbl 1054.05051 Discuss. Math., Graph Theory 24, No. 1, 109-114 (2004). Summary: We describe some new applications of nonabelian \(pq\)-groups to construction problems in graph theory. The constructions include the smallest known trivalent graph of girth 17, the smallest known regular graphs of girth five for several degrees, along with four edge colorings of complete graphs that improve lower bounds on classical Ramsey numbers. Cited in 2 Documents MSC: 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) 05C35 Extremal problems in graph theory 05C55 Generalized Ramsey theory Keywords:Ramsey number; edge coloring; cage; degree; girth; Cayley graph PDFBibTeX XMLCite \textit{G. Exoo}, Discuss. Math., Graph Theory 24, No. 1, 109--114 (2004; Zbl 1054.05051) Full Text: DOI