منابع مشابه
Extremal Problems in Digraphs
Let G be a finite simple directed graph on n vertices. Say G is m-free if it has no directed cycles of length at most m. In 1978, Caccetta and Häggkvist [3] conjectured that if G has minimum out-degree at least r, then G is not dn/re-free. Finding upper bounds on the minimum out-degree in 3-free digraphs has been of particular interest in recent research. In this thesis, we present new results ...
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In this paper, we establish several theorems involving configurations of points and lines in the Euclidean plane. Our results answer questions and settle conjectures of P. Erd6s, G. Purdy, and G. Dirac. The principal result is that there exists an absolute constant cl so that wlaen V'n<=t~_[T], the number of incidences between n points and t lines is less than c~n~/3t ""/3. Using this restllt, ...
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I would like to illustrate the problems which I shall investigate in this paper by an example. Denote by r&z) the maximum number of integers not exceeding n, no k of which form an arithmetic progression. The problem is to determine or estimate the value of rk(n). This problem is connected with several known questions of number theory. If r&) <(I-t)n/log n for every K, if n is sufficiently large...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
سال: 1992
ISSN: 0263-6115
DOI: 10.1017/s1446788700032882