New Examples of Graphs without Small Cycles and of Large Size
نویسندگان
چکیده
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) andH5(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 familyH3(p) for q = p ≥ 3. Then we show that no member of the second family H5(p) is a subgraph of a generalized 6–gon. Then, for infinitely many values of q, we construct a new infinite series of bipartite q–regular edge–transitive graphs of order 2q and girth 10. Finally, for any prime power q ≥ 3, we construct a new infinite series of bipartite q–regular edge–transitive graphs of order 2q and girth g ≥ 14. Our constructions were motivated by some results on embeddings of Chevalley group geometries in the corresponding Lie algebras and a construction of a blow–up for an incident system and a graph.
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ورودعنوان ژورنال:
- Eur. J. Comb.
دوره 14 شماره
صفحات -
تاریخ انتشار 1993