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A counterexample to a conjecture of Schwartz

Abstract:

In 1990, motivated by applications in the social sciences, Thomas Schwartz made a conjecture about tournaments which would have had numerous attractive consequences. In particular, it implied that there is no tournament with a partition A, B of its vertex set, such that every transitive subset of A is in the out-neighbour set of some vertex in B, and vice versa. But in fact there is such a tournament, as we show in this article, and so Schwartz' conjecture is false. Our proof is non-construct...

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Publication status:
Published

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Publisher copy:
10.1007/s00355-011-0638-y

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Journal:
SOCIAL CHOICE AND WELFARE
Volume:
40
Issue:
3
Pages:
739-743
Publication date:
2013-03-05
DOI:
EISSN:
1432-217X
ISSN:
0176-1714
URN:
uuid:6d003250-c14e-4400-87c9-f1aa5f77af12
Source identifiers:
379818
Local pid:
pubs:379818
Language:
English

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