New Examples of Graphs without Small Cycles and of Large Size

  title={New Examples of Graphs without Small Cycles and of Large Size},
  author={Felix Lazebnik and Vasiliy A. Ustimenko},
  journal={Eur. J. Comb.},
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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Showing 1-10 of 24 references

Simple Groups of Lie Type

  • R. W. Carter
  • 1972
Highly Influential
5 Excerpts

A linear interpretation of the flag geometries of Chevalley groups

  • V. A. Ustimenko
  • Kiev University. Translated from Ukrainskii…
  • 1990
Highly Influential
5 Excerpts

Division algebras and Tits geometries, DAN

  • V. A. Ustimenko
  • USSR, V. 296,
  • 1987
Highly Influential
4 Excerpts

Extermal Graph Theory. In “Selected Topics in Graph Theory 2

  • M. Simonovits
  • 1983
Highly Influential
6 Excerpts

Constructing random–like graphs. In “Probabilistic Combinatorics and its Applications.

  • Fan K. Chung
  • Lecture Notes, A.M.S.., San Francisco,
  • 1991
1 Excerpt

Sós , On a problem of graph theory

  • A. Rényi P. Erdös, T. V.
  • Studia Sci . Math . Hungar .
  • 1991

On the embeddings of some geometries and flag systems in Lie algebras and superalgebras, in Root systems, representation and geometries, Kiev

  • V. A. Ustimenko
  • IM AN UkrSSR,
  • 1990
3 Excerpts

Brown , On graphs that do not contain a Thomsen graph , Canad

  • G. W.
  • Math . Bull .
  • 1989

Constructions of telephone networks by group representations

  • F. Bien
  • Notices Amer. Math. Soc
  • 1989
1 Excerpt

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