Extremal properties of regular and affine generalized m-gons as tactical configurations

@article{Ustimenko2003ExtremalPO,
  title={Extremal properties of regular and affine generalized m-gons as tactical configurations},
  author={Vasiliy A. Ustimenko and Andrew J. Woldar},
  journal={Eur. J. Comb.},
  year={2003},
  volume={24},
  pages={99-111}
}
The purpose of this paper is to derive bounds on the sizes of tactical configurations of large girth which provide analogues to the well-known bounds on the sizes of graphs of large girth. Let exα(v, g) denote the greatest number of edges in a tactical configuration of order v, bidegreea, aα and girth at least g. We establish the upper bound exα(v, g) = O(v1+ 1 τ ), whereτ = 4(α + 1)g − 1 for g ≡ 0(mod 4) andτ = 4(α + 1)g + 2(α − 3) for g ≡ 2(mod 4). We further demonstrate this bound to be… CONTINUE READING