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, Volume 8, Issue 4, pp 349–358 | Cite as

Multiplicative posets

  • N. W. Sauer
  • Xuding Zhu
Article

Abstract

A functionf from the posetP to the posetQ is a strict morphism if for allx, y ∈ P withx<y we havef(x)<f(y). If there is such a strict morphism fromP toQ we writeP → Q, otherwise we writeP\(\not \to \)Q. We say a posetM is multiplicative if for any posetsP, Q withP\(\not \to \)M andQ\(\not \to \)M we haveP ×Q\(\not \to \)M. (Here (p1,q1)<(p2,q2) if and only ifp1<p2 andq1<q2.) This paper proves that well-founded trees with height ≤ω are multiplicative posets.

Mathematics Subject Classification (1991)

06A06 

Key words

Posets strict morphisms multiplicativity Hedetniemi's conjecture 

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References

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    M.El-Zahar and N. W.Sauer (1985) The chromatic number of the products of two 4-chromatic graphs is 4,Combinatorica 5(2), 121–126.Google Scholar
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    R.Haggkvist, P.Hell, D. J.Miller, and V. N.Lara (1988) On multiplicative graphs and the product conjecture,Combinatorica 8(1), 63–74.Google Scholar
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    S. T. Hedetniemi (1966) Homomorphisms of graphs and automata, University of Michigan Technical Report 03105-44-T.Google Scholar
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    P. Hell, H. Zhou, and X. Zhu (1991) Multiplicative oriented cycles. Manuscript.Google Scholar

Copyright information

© Kluwer Academic Publishers 1992

Authors and Affiliations

  • N. W. Sauer
    • 1
  • Xuding Zhu
    • 1
  1. 1.Department of Mathematics and StatisticsThe University of CalgaryCalgaryCanada

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