Short certificates for tournaments

Noga Alon; Miklós Ruszinkó

Short certificates for tournaments

Noga Alon, Miklós Ruszinkó

Research output: Contribution to journal › Article › peer-review

Abstract

An isomorphism certificate of a labeled tournament T is a labeled subdigraph of T which together with an unlabeled copy of T allows the errorless reconstruction of T. It is shown that any tournament on n vertices contains an isomorphism certificate with at most n log₂ n edges. This answers a question of Fishburn, Kim and Tetali. A score certificate of T is a labeled subdigraph of T which together with the score sequence of T allows its errorless reconstruction. It is shown that there is an absolute constant ∈ > 0 so that any tournament on n vertices contains a score certificate with at most (1/2 - ∈)n² edges.

Original language	English
Pages (from-to)	XXIX-XXX
Journal	Electronic Journal of Combinatorics
Volume	4
Issue number	1
State	Published - 1 Dec 1997
Externally published	Yes

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics
Applied Mathematics

Cite this

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AB - An isomorphism certificate of a labeled tournament T is a labeled subdigraph of T which together with an unlabeled copy of T allows the errorless reconstruction of T. It is shown that any tournament on n vertices contains an isomorphism certificate with at most n log2 n edges. This answers a question of Fishburn, Kim and Tetali. A score certificate of T is a labeled subdigraph of T which together with the score sequence of T allows its errorless reconstruction. It is shown that there is an absolute constant ∈ > 0 so that any tournament on n vertices contains a score certificate with at most (1/2 - ∈)n2 edges.

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Short certificates for tournaments

Abstract

ASJC Scopus subject areas

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