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Title of article :
Extremal properties of regular and affine generalized m-gons as tactical configurations
Author/Authors :
Ustimenko، نويسنده , , V.A and Woldar، نويسنده , , A.J.، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2003
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Abstract :
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, bidegree a, aα and girth at least g. We establish the upper bound exα(v,g)=O(v1+1τ), where τ=14(α+1)g−1 for g≡0(mod4) and τ=14(α+1)g+12(α−3) for g≡2(mod4). We further demonstrate this bound to be sharp for the regular and affine generalized m-gons but not for the nonregular generalized m-gons. Finally, we derive lower bounds on exα(v,g) via explicit group theoretic constructions.
Keywords :
Generalized m-gon , girth , Affine m-gon , Tactical configuration , Bidegree , Free product , Rainbow graph , Bipartite biregular graph , Group rainbow graph , filtration , Unipotent-like factorization
Journal title :
European Journal of Combinatorics
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