TY - JOUR

T1 - Algorithmic solution of extremal digraph problems

AU - Brown, W. G.

AU - Erdős, P.

AU - Simonovits, M.

PY - 1985

Y1 - 1985

N2 - For a given family ℒ of digraphs, we study the “extremal” digraphs on n vertices containing no member of ℒ, and having the maximum number of arcs, ex(formula presented). We resolve conjectures concerning the set (formula presented) (formula presented) ranges over all possible families, and describe a “finite” algorithm that can determine, for any ℒ, all matrices A for which a sequence A(n)of “matrix digraphs” is asymptotically extremal (A(n) contains no member of and has ex(formula presented).

AB - For a given family ℒ of digraphs, we study the “extremal” digraphs on n vertices containing no member of ℒ, and having the maximum number of arcs, ex(formula presented). We resolve conjectures concerning the set (formula presented) (formula presented) ranges over all possible families, and describe a “finite” algorithm that can determine, for any ℒ, all matrices A for which a sequence A(n)of “matrix digraphs” is asymptotically extremal (A(n) contains no member of and has ex(formula presented).

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U2 - 10.1090/S0002-9947-1985-0808730-0

DO - 10.1090/S0002-9947-1985-0808730-0

M3 - Article

AN - SCOPUS:84967781629

VL - 292

SP - 421

EP - 449

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 2

ER -