Geodesic
Some applications of pq-groups in graph theory
Discussiones Mathematicae. Graph Theory, Tome 24 (2004) no. 1, pp. 109-114

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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.
Keywords: Ramsey number, edge coloring, cage, degree, girth, Cayley graph 
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Exoo, Geoffrey. Some applications of pq-groups in graph theory. Discussiones Mathematicae. Graph Theory, Tome 24 (2004) no. 1, pp. 109-114. http://geodesic.mathdoc.fr/item/DMGT_2004_24_1_a8/