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 |