Zentralblatt MATH
Publications of (and about) Paul Erdös
Zbl.No: 607.05040
Autor: Brown, William G.; Erdös, Paul; Simonovits, M.
Title: Algorithmic solution of extremal digraph problems. (In English)
Source: Trans. Am. Math. Soc. 292, 421-449 (1985).
Review: For a given family L of digraphs, the maximum number ex(n,L) of arcs a digraph on n vertices containing no member of L can possesses and the set Ex(n,L) of digraphs which attain this maximum are studied. In particular, the asymptotic behaviour of ex(n,L)/n2 is discussed in detail.
For a square matrix A, a sequence A(n) of digraphs, called matrix digraphs, are defined which are of, in some sense, simple structure. An algorithm is given to determine all matrices A such that each A(n) contains no member of L, and has ex(n,L)+o(n2) arcs as n ––> oo.
Reviewer: Z.Ma
Classif.: * 05C35 Extremal problems (graph theory)
05C20 Directed graphs (digraphs)
Keywords: digraphs
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