Let s(n) be the threshold for which each directed path of order smaller than s(n) is extendible from one of its endpoints in some tournament T-n. It is shown that s(n) is asymptotic to 3n/4, with an error term at most 3 for infinitely many n. There are six tournaments with s(n) = n. (C) 1996 John Wiley & Sons, Inc.
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Department of Mathematics, ETH Zurich, Zurich, SwitzerlandDepartment of Mathematics, ETH Zurich, Zurich, Switzerland
Draganić, Nemanja
Dross, François
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Université de Bordeaux, CNRS, Bordeaux INP, LaBRI, UMR 5800, Talence, FranceDepartment of Mathematics, ETH Zurich, Zurich, Switzerland
Dross, François
Fox, Jacob
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Department of Mathematics, Stanford University, Stanford,CA, United StatesDepartment of Mathematics, ETH Zurich, Zurich, Switzerland
Fox, Jacob
Girão, António
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Institut für Informatik, Universität Heidelberg, GermanyDepartment of Mathematics, ETH Zurich, Zurich, Switzerland
Girão, António
Havet, Frédéric
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CNRS, Université Côte d’Azur, I3S, INRIA, Sophia Antipolis, FranceDepartment of Mathematics, ETH Zurich, Zurich, Switzerland
Havet, Frédéric
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Korándi, Dániel
Lochet, William
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Department of Informatics, University of Bergen, NorwayDepartment of Mathematics, ETH Zurich, Zurich, Switzerland
Lochet, William
Correia, David Munhá
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Department of Mathematics, ETH Zurich, Zurich, SwitzerlandDepartment of Mathematics, ETH Zurich, Zurich, Switzerland
Correia, David Munhá
Scott, Alex
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Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, United KingdomDepartment of Mathematics, ETH Zurich, Zurich, Switzerland
Scott, Alex
Sudakov, Benny
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Department of Mathematics, ETH Zurich, Zurich, SwitzerlandDepartment of Mathematics, ETH Zurich, Zurich, Switzerland
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Univ Amsterdam, Korteweg de Vries Inst Math, POB 94248, NL-1090 GE Amsterdam, NetherlandsUniv Birmingham, Sch Math, Birmingham B15 2TT, W Midlands, England
Patel, Viresh
Skokan, Jozef
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London Sch Econ, Dept Math, Houghton St, London WC2A 2AE, England
Univ Illinois, Dept Math, Urbana, IL 61801 USAUniv Birmingham, Sch Math, Birmingham B15 2TT, W Midlands, England
Skokan, Jozef
Talbot, John
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Univ London Univ Coll, Dept Math, London WC1E 6BT, EnglandUniv Birmingham, Sch Math, Birmingham B15 2TT, W Midlands, England