Pii: S0012-365x(98)00314-8
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چکیده
Given a partially ordered set P = (X,P), a function F which assigns to each x E X a set F(x) so that x ~ 2, some posets of arbitrarily large dimension have inclusion representations using spheres in R a. However, using a theorem of Alon and Scheinerman, we know that not all posets of dimension d ÷ 2 have inclusion representations using spheres in R a. In 1984, Fishbum and Trotter asked whether every finite 3-dimensional poset has an inclusion representation using spheres (circles) in R 2. In 1989, Brightwell and Winkler asked whether every finite poset is a sphere order and suggested that the answer was negative. In this paper, we settle both questions by showing that there exists a finite 3-dimensional poset which is not a sphere order. The argument requires a new generalization of the Product Ramsey Theorem which we hope will be of independent interest. @ 1999 AT&T; Information Services. Published by Elsevier Science B.V. All rights reserved A M S classification." 06A07; 05C35
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Maximal sets of mutually orthogonal Latin squares
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We consider the operation of summation of two graphs G~ and G2. Necessary and sufficient conditions for G1 + G2 to be perfect are derived. (~) 1999 Elsevier Science B.V. All rights reserved
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تاریخ انتشار 1999