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Some applications of \(pq\)-groups in graph theory. (English) Zbl 1054.05051

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.

MSC:

05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
05C35 Extremal problems in graph theory
05C55 Generalized Ramsey theory
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