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# New Examples of Graphs without Small Cycles and of Large Size

@article{Lazebnik1993NewEO, title={New Examples of Graphs without Small Cycles and of Large Size}, author={Felix Lazebnik and Vasiliy A. Ustimenko}, journal={Eur. J. Comb.}, year={1993}, volume={14}, pages={445-460} }

- Published 1993 in Eur. J. Comb.
DOI:10.1006/eujc.1993.1048

For any prime power q ≥ 3, we consider two infinite series of bipartite q–regular edge–transitive graphs of orders 2q and 2q which are induced subgraphs of regular generalized 4–gon and 6–gon, respectively. We compare these two series with two families of graphs, H3(p) and H5(p), p is a prime, constructed recently by Wenger ([26]), which are new examples of extremal graphs without 6– and 10–cycles respectively. We prove that the first series contains the family H3(p) for q = p ≥ 3. Then we show… CONTINUE READING

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