New examples of graphs without small cycles and of large size
European Journal of Combinatorics - Special issue: association schemes
Graphs of prescribed girth and bi-degree
Journal of Combinatorial Theory Series B
Explicit construction of graphs with an arbitrary large girth and of large size
Discrete Applied Mathematics - Special volume: Aridam VI and VII, Rutcor, New Brunswick, NJ, USA (1991 and 1992)
A characterization of the components of the graphs D(k,q)
Proceedings of the 6th conference on Formal power series and algebraic combinatorics
New lower bounds on the multicolor Ramsey numbers rk(C4)
Journal of Combinatorial Theory Series B
Performance of algebraic graphs based stream-ciphers using large finite fields
Annales UMCS, Informatica - Cryptography and data protection
On LDPC codes corresponding to affine parts of generalized polygons
Annales UMCS, Informatica - Cryptography and data protection
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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) = 0(v1+1/τ), where τ = 1/4(α + 1)g -1 for g = 0(mod 4) and τ = 1/4(α + 1)g + ½(α - 3) for g ≡ = 2(mod 4). 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.