# pairwise disjoint

## pairwise disjoint

[¦per‚wīz dis′jȯint]
(mathematics)
The property of a collection of sets such that no two members of the collection have any elements in common.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Suppose [V.sub.1],..., [V.sub.m-1] are pairwise disjoint sets in L = V U.
Among their problems are the Erdos-Ko-Rado theorem via shifting, the Kleitman theorem for no s pairwise disjoint sets, uniform measure versus product measure, F'rude's structure theorem, some algebraic constructions for L systems, and a cross intersection problem with measures.
A simply connected proper subdomain D of the complex domain C is said to be convex if the linear segment joining any two points of D lies entirely in D and is said to be close-to-convex if its complement in C is the union of closed half-lines with pairwise disjoint interiors.
Then there exists a sequence {[z.sub.n]} in [<[x.sub.0]>.sub.R] such that {[tau]([z.sub.n]) : [tau] [member of] [OMEGA](Z)} [subset] [0, 1], for each n [member of] N, and [mathematical expression not reproducible] is a sequence of nonempty pairwise disjoint subsets of [OMEGA](Z).
Then for any continuous map f : [[DELTA].sub.N] [right arrow] [R.sup.d],for each j = 1,..., k, there are r = [q.sub.j][r.sub.j] pairwise disjoint faces [mathematical expression not reproducible] such that
If a finite number of pairwise disjoint open intervals ([a.sub.k], [b.sub.k]), k = 1, 2, ..., n, are contained in the open interval (A, B), then
All operations maintain the invariants that (1) the segments in I are pairwise disjoint, and (2) the remaining horizontal segments in I form an independent set in the bar visibility graph (of all horizontal segments in the current rectangulation).
We can easily see, by the same method as the proof of Theorem A, that if n + 1 meromorphic functions on C share q pairwise disjoint n-point sets IM, then at least two of them are identical (see, also, Theorem 4).
A plane matching is a plane graph consisting of pairwise disjoint edges.
Note that Ka is a minor of a graph Gif and only if there is a collection {S : A3/4 ca} of nonempty connected and pairwise disjoint subsets of V (G ) such that for all A3/4 y ca with A3/4 s y the sets SA3/4 and Sy are connected to each other.
(i) [J.sub.0], [J.sub.1], ..., [J.sub.p-2] [subset] ([lambda], 1] are pairwise disjoint;
Furthermore, we can partition the edge set of [K.sub.n,n] into n pairwise disjoint perfect matchings [M.sub.0], [M.sub.1], ...,[M.sub.n-1] such that M; is exactly the set of edges of bipartite difference i in [K.sub.n,n] for i [member of] [0, n - 1].

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