منابع مشابه
Judicious partitions of uniform hypergraphs
The vertices of any graph with m edges can be partitioned into two parts so that each part meets at least 2m 3 edges. Bollobás and Thomason conjectured that the vertices of any r-uniform graph may be likewise partitioned into r classes such that each part meets at least cm edges, with c = r 2r−1 . In this paper, we prove this conjecture for the case r = 3. In the course of the proof we shall al...
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Article history: Received 20 May 2008 Available online 21 August 2009
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Let ~r = (ri) n i=1 be a sequence of real numbers of length n with sum s. Let s0 = 0 and si = r1 + . . . + ri for every i ∈ {1, 2, . . . , n}. Fluctuation theory is the name given to that part of probability theory which deals with the fluctuations of the partial sums si. Define p(~r) to be the number of positive sum si among s1, . . . , sn and m(~r) to be the smallest index i with si = max 06k...
متن کاملJudicious Partitions of 3-uniform Hypergraphs
A conjecture of Bollobás and Thomason asserts that, for r ≥ 1, every r-uniform hypergraph with m edges can be partitioned into r classes such that every class meets at least rm/(2r−1) edges. Bollobás, Reed and Thomason [3] proved that there is a partition in which every edge meets at least (1 − 1/e)m/3 ≈ 0.21m edges. Our main aim is to improve this result for r = 3. We prove that every 3-unifor...
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By K n we denote the complete k-uniform hypergraph of order n, 1 6 k 6 n−1, i.e. the hypergraph with the set Vn = {1, 2, ..., n} of vertices and the set ( Vn k ) of edges. If there exists a permutation σ of the set Vn such that {E, σ(E), ..., σq−1(E)} is a partition of the set ( Vn k ) then we call it cyclic q-partition of K n and σ is said to be a (q, k)-complementing. In the paper, for arbitr...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1981
ISSN: 0002-9947
DOI: 10.2307/1998342